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American companies are starting to test the extent of their pricing power.

Faced with rising costs for materials, transportation and workers, companies are charging more for products from metal fasteners to Oreo cookies, helping fuel inflation like the U.S. hasnt seen in more than a decade.

As customers accept the price hikes, some big companies said they expect to raise prices even more. Others are more cautious, unsure if U.S. consumers have the appetite to absorb additional increases.

What companies decide will go a long way to answering a question that has surged to the top of executives and economists agendas this year: Is the recent jump in inflation transitory, as the Federal Reserve predicts, or persistent, as some executives warn?

Fastenal Co. , a major distributor of industrial supplies such as nuts and bolts, and Conagra Brands Inc., a food conglomerate, illustrate the pricing dance playing out across the biggest U.S. firms. Both companies are passing along higher costs to customers. They have different views about what happens next.

Fastenal charged its customers enough extra in the first half of the year to offset its own higher product costs. But the company warns its ability to keep pace with costs could lag in coming months, in part because customer contracts put limits on price increases.

In an environment where inflation continues to rise quarter after quarter after quarter, there are certain sticking points within our ability to push it through, said Fastenal finance chief Holden Lewis. Inflation in the marketplace can rise at a much more methodical and smooth pace than our ability to change prices can.

Conagra, which makes Birds Eye frozen vegetables and Slim Jim meat snacks, among hundreds of other food products, couldnt raise prices enough in the most recent quarter to make up for its own rising costs, including for cooking oils, packaging and transportation. It expects price increases and other measures to offset its costs later this year, and said it might need to raise prices further.

We still think our products price points have room to move north based on the quality that we offer, Chief Executive Sean Connolly told investors last week, noting that widespread increases across grocery aisles seem to leave consumers more willing to pay so far. You dont generally get a customer to accept inflation-justified pricing until theyre confident its not transitory inflation, he said.

How hard companies continue to push to raise prices, and how well they succeed, is at the heart of the current concern about inflation. The more companies succeed, the more traction price inflation is likely to gain, keeping prices high and rising. If the price increases falter, inflation is likely to ease as labor and supply shortages diminish and the pandemics economic effects recede.

Of about a dozen large U.S. companies examined by The Wall Street Journal, most said they have succeeded in raising at least some prices but are unsure whether they can continue to do so. Several said they plan or hope to push additional price increases through.

I dont think anyone knows what the word transitory is really going to turn out to mean, said Julien Mininberg, who heads consumer-products company Helen of Troy Ltd.

The maker of Pert shampoo and OXO potato peelers, Helen of Troy said it has raised prices selectively, including by introducing new products at higher price points. The company said it slowed price increases in its health and home division while working through some regulatory issues.

Before long, it plans to go back to the customers and take those prices up, Mr. Mininberg said in a July 8 conference call with investors.

Like many companies, Helen of Troy is combining price increases with other strategies to manage its own rising costs.

It has been building up inventory for the coming busy season ahead of recent cost increases in the market and using prenegotiated shipping rates that are below current prices, Mr. Mininberg said. The company expects to absorb $55 million to $60 million of inflation-related cost increases in the fiscal year ending in February.

European consumer-products giant Unilever PLC, which sells Dove soaps and Lipton tea, on Thursday said it would also raise prices beyond a 1.6% increase in the second quarter. Its shares fell on news that higher costs would likely eat into profits.

Most economists expect inflation to decline from its current 13-year high but are divided on when, or whether, it will fall enough to satisfy the Fed. The consumer-price index was up 5.4% in June from a year earlier.

The central banks preferred gauge, the price index of personal consumption expenditures, gained 3.9% in May from a year earlier. Fed officials in June projected this measure of inflation would ease to 3.4% by this years fourth quarter, and to 2.1% by the end of next yearnear the Feds 2% target.

Economists surveyed this month by The Wall Street Journal also anticipate a decline from current levels but expect more inflation than the Fed. The median forecast anticipates 2.3% inflation by the fourth quarter of 2022, down from an annual rate of 3.7% in the fourth quarter of this year, also using the PCE index.

A University of Michigan survey conducted in late June through mid-July found that the median consumer expects prices to rise 4.8% over the next 12 months, a 12-year high.

All this points to the prospects of inflation running higher over the next year than it has for a long time.

In a poll of 606 U.S. businesses across industries, 33% said they are raising prices, while just 4% said they are cutting them, according to 451 Research, a unit of financial data firm S&P Global Market Intelligence. Retail and manufacturing businesses led the way, with 44% and 41%, respectively, increasing prices.

Chipotle Mexican Grill Inc. raised its menu prices by around 4% earlier this year, on top of increases the chain made on the price of delivered food last year. On Tuesday, the burrito chain said it hasnt seen pushback from customers, and it believes it is proving its pricing power with diners.

I actually see it as a long term strength of the company, said CEO Brian Niccol. The companys own freight and avocado costs are up.

Chipotle hasnt yet decided whether to further lift prices. The company shifted to an average wage of $15 an hour last month, which it said hit second-quarter margins. More of those increased labor costs are expected to trickle into results during the current quarter.

Food companies are raising prices as commodity costs rise, and a number of them appear bullish on prospects for further increases.

Snack giant Mondelez International Inc. raised prices on Oreo cookies and other snacks this year, and told investors last month it is considering price increases for 2022 based on the commodity cost inflation it expects. That could mean smaller packages bearing the same price tag, or less discounting, both of which serve to raise the companys average selling price.

Several brands said their planned price increases wont be fully implemented in grocery stores until the second half of this year. Price increases by Hormel FoodsCorp. for products including its Jennie-O ground turkey and Skippy peanut butter so far havent covered the companys higher costs for peanuts, oil and plastic containers, among other inputs, the Austin, Minn., company said. It expects more price increases later this year.

General Mills Inc. CEO Jeff Harmening, whose company makes Betty Crocker cake mixes and Cheerios cereal, said unusually high consumer savings might make Americans less sensitive to price increases than usual. Still, he added, they could cut back on food spending if companies raise prices too far. The next few months will be especially critical, Mr. Harmening said.

The company has said price increases and reduced discounting will be used to offset less than half its increased costs, with internal cuts and efficiencies making up most of the rest.

The companys primary response to inflation is to become more efficient, General Mills spokeswoman Kelsey Roemhildt said. But inflation is so high right now that productivity alone wont solve it, she added. Given the level of inflation that we forecast for the fiscal year, we will be using all tools in our pricing tool kit, includinglist price increases where needed, she said.

Some high-profile executives in the financial industry have cited a range of factors suggesting that higher inflation will persistwith caveats. Larry Fink, CEO of asset-management giant BlackRock Inc., has pointed to the shift in emphasis in Washington in recent years away from expanding global trade and toward creating domestic jobs, rebuilding U.S. manufacturing and various national-security issues.

Jamie Dimon, CEO of JPMorgan Chase & Co., also said higher inflation is possible as jobs proliferate and wages risebut added that robust economic growth could more than offset the impact.

Mike Jackson, CEO of AutoNation Inc., the nations largest car dealership by sales, chalked up inflationary pressures in his industry largely to higher unemployment benefits related to the pandemic recovery, which helped push employee wages up, and a jump in used-vehicle values compared with a year ago when rental-car companies were liquidating their fleets.

I very much agree with the view of the Federal Reserve, which is that you have some unique circumstances at the moment, said Mr. Jackson, who has served on the board of the Federal Reserve Bank of Atlanta. We have a transitory situation here, and things will look different by the end of the year.

If companies really believed price increases will persist, they would start expanding operations, to reflect the expectation of continued higher prices, said Steven Blitz, chief U.S. economist of research company TS Lombard. He said he hasnt seen it yet.

Theyre enjoying demand, theyre enjoying the high prices theyre getting, but I dont see them leveraging their businesses to double production, Mr. Blitz said. So far, he added, theyre telling you they dont trust what they see as permanent.

Still, some executives do see longer-term price pressure, even beyond consumer sectors. Jeff Miller, chief executive of Halliburton Co. , the worlds second-largest oil-field service company, said during its second-quarter earnings call, that the company has been able to pass along to its oil-company customers its own increased costs for maintenance, parts and labor. He predicted a multiyear upturn in oil-patch activity, the first in seven years, and said equipment prices are already rising in North America.

Conagra, which has raised prices on its Armour Star canned meat line as protein and steel costs have risen, has watched as consumers accept higher prices across supermarket aisles. Grocery prices rose 0.8% in June from May, compared with the 0.4% month-to-month increase in the two prior periods, the Labor Department said.

I think you call it strength in numbers, Mr. Connolly, the CEO, said in response to an analyst question. He said he believes consumers are likely to be more accepting of higher prices due to their ubiquity throughout the supermarket, and that the relative affordability of groceries over restaurant food also helps.

Conagra executives said they expect inflationary cost pressures to be the worst in the companys first quarter, ending this August, after which profit margins are expected to improve as price increases on its products take effect, along with productivity improvements and other cost savings, and the rate of inflation slows. As inflation persists, it becomes harder to manage, Conagra executives added.

Fastenal is leaning on price-management skills it honed in recent years managing cost increases sparked by tariffs. The company realized it needed to address price changes more tactfully, in part because customers were reluctant to swallow broad increases. To help navigate pricing changes, Fastenal uses data to show how it sources specific products and why prices are changing, said Mr. Lewis, the CFO. The result: customers are more likely to accept targeted price increases.

Although Fastenals spending on metal, transportation and fuel has risen, its price increases have been smaller, because those inputs make up only part of its production expenses.

Cost of goods has many, many components, not all of which are inflating, Mr. Lewis said. Demand for the companys products remains strong, and he doesnt see signs of inflation abating right now, but he admits to having little visibility into the future. Many of Fastenals customers are under contracts, some of which limit the companys ability to raise prices, and it is difficult to constantly adjust prices to those customers that arent under contract. If we raise prices on fasteners in June, it can be hard to come back in July, he said.

We think that we will be able to offset that [cost] inflation, he said. But the pace and timing of that depends very much on how the market continues to evolve around inflation and pricing and those sorts of things. Its a pretty dynamic environment.