America’s largest frackers are reporting huge profits but plan to keep oil production in low gear this year, adhering to an agreement with Wall Street, even as prices approach the $100-a-barrel mark for the first time since 2014.

Three of the largest shale companies, Pioneer Natural Resources Co. PXD 1.41% Devon DVN -0.85% Energy Corp. and Continental Resources Inc., CLR -2.17% this week reported their highest annual profits in more than a decade for 2021. The companies said they collected record amounts of extra cash by hanging on to the money they earn selling oil and natural gas and reinvesting only what they needed to keep output roughly flat. All three said they would continue to limit production growth this year.

They are pledging austerity despite a tightening oil-market supply. Global oil-production growth isn’t keeping pace with renewed demand as economies recover from the pandemic, and the threat of a Russian invasion of Ukraine is rattling markets. Those dynamics have alarmed the White House, which has asked U.S. producers to drill more as it confronts soaring gasoline prices and broad inflation.

For now, most large shale companies aren’t answering the White House’s call, sticking to commitments they made to limit production and return more cash to shareholders, an effort to win back investors who fled the industry after years of poor returns.

U.S. oil prices fell almost 1% Friday to $91.07 per barrel.

Oklahoma-based Devon, the top performer in the S&P 500 last year, said it has expanded a share-buyback program by 60% and raised its dividend to a record level. The company also said it collected $2.8 billion in profit last year, its highest since 2007. Devon expects costs to rise 15% because of inflation and supply-chain disruptions but aims to pump about the same amount of oil as last year.

“I want to be clear that there is no change to our cash-return playbook,” Devon Chief Executive Richard Muncrief told investors Wednesday. “It will be more of the same.”

Analysts disagree about how much U.S. oil production will rise in response to high prices this year, amid a supply vacuum left by the Organization of the Petroleum Exporting Countries and its allies, collectively known as OPEC+, which haven’t kept up with a goal set last year to add 400,000 barrels a day to the market each month.

While forecasts vary widely, many analysts expect growth to be concentrated in the Permian Basin of West Texas and New Mexico, by far the most active U.S. oil field, driven by private companies and the two U.S. oil majors, Exxon Mobil Corp. and Chevron Corp. CVX -0.14% But most big shale companies plan to keep production roughly flat overall.

The average number of drilling rigs run by private oil producers rose to 323 so far in February, up 127% from the start of last year, according to energy data analytics firm Enverus. Meanwhile, rigs operated by large and midsize publicly traded oil producers rose about 28% to 215 over the same period.

Mr. Muncrief said he expects output to rise in the Permian, but not rapidly, and that it is likely “going to be the only place in the U.S. you truly even see much growth.”