By Eric Morath, Wall Street Journal–

Filings for jobless benefits fell last week to their lowest level since March, a sign layoffs eased somewhat as the labor market tries to recover from the coronavirus pandemic.

Initial unemployment claims fell by a seasonally adjusted 249,000 to 1.2 million for the week ended Aug. 1, the Labor Department said Thursday. The decline came as an extra $600 a week in pandemic-related unemployment benefits ended.

The number of applications last week was the lowest since the pandemic struck the U.S. Weekly claims figures, however, remain well above the pre-pandemic record of 695,000 in 1982. Before last week, applications had plateaued in recent weeks, halting what had been a steady decline from a peak of 6.9 million in late March, when the pandemic and business closures shut down parts of the U.S. economy.

The number of people receiving benefits through regular state programs, which cover the majority of workers, decreased by 844,000 to 16.1 million for the week ended July 25. Those continuing claims, reported with a week lag, fell to lowest level since April.

“The labor market is still under water,” said Monica Garcia-Perez, a labor economist at St. Cloud State University in Minnesota.

After employers shed 21 million jobs earlier this year, hiring surged in May and June, adding a combined 7.5 million jobs, according to the Labor Department. That was largely because workers temporarily laid off were recalled, she said. Ms. Garcia-Perez said gains aren’t likely to persist at that rate, and the future path of hiring will be closely tied to whether or not the virus is controlled and people have confidence to resume normal activities. “If we see a new wave of cases this fall and new restrictions, you’ll see layoffs move back up,” she said.

The Labor Department will release its broadest picture of July employment on Friday in the monthly jobs report. Economists surveyed by The Wall Street Journal forecast the report to show 1.5 million jobs were added last month and the unemployment rate fell to 10.6% from 11.1% in June. While those would be historically strong gains, they would also be a marked slowdown from the pace of the prior two months with unemployment still well above pre-pandemic levels.

Other data also point to an easing of hiring. Payroll processor ADP said Wednesday private-sector payrolls grew by 167,000 last month. Employees reported for 1% more shifts in July from the month before, a slowdown from a 5.9% increase in June and an 8.7% gain in May, according to Kronos, a Massachusetts workforce management software company. The number of job postings remains well below last year, according to job-search site Indeed.com.

The figures collectively indicate many people are still losing their jobs months after the pandemic-induced economic downturn began.

Shana O’Mara has been receiving unemployment benefits since early July, after the expiration of a government loan that was sustaining her Tempe, Ariz., travel agency. She stopped drawing a salary from her business to keep it alive, but has continued to work without pay helping customers rebook and cancel trips.

She said her most recent weekly unemployment benefit payment fell to $214 after taxes, from $748 the preceding week, reflecting the July 31 expiration of an additional $600 in pretax federal benefits.

“I don’t think anyone can live on $800 a month,” she said. Her family has stopped ordering takeout, and she called her auto lender and credit-card issuers asking for deferrals. She said the enhanced benefits allowed her to keep serving her clients, rather than seek out a job. For now, she is trying to keep her business, the Pixie Planner, afloat until more customers want to travel to Disney World and board cruise ships.

“It’s hard to see the end of this,” she said. “And it’s especially frustrating because it doesn’t feel like we have the support of our government.”

Still, some businesses say they are struggling to find workers despite historically high unemployment.

Key Staffing in Topeka, Kan., is seeking to fill customer-service, accounting and warehouse jobs, said Chief Executive Patti Mellard. She said the staffing firm has seen an increase in applicants in the past week since unemployment benefits have been reduced. But she said some prospective workers are concerned about becoming ill with the virus or say they don’t have available child care.

One option is customer-service jobs, which can be done at home. Those jobs start at $12 to $15 an hour, she said. That is slightly less than a person would have received on enhanced unemployment benefits that expired at the end of July.

Some workers who don’t qualify for benefits under regular state programs—such as the self-employed, gig workers, parents who can’t find child care—are able to tap unemployment benefits under a law passed in March. Those programs continue through the end of the year, but at a lower payment level with the expiration of the $600 enhancement.

Nearly the same level of workers received aid last month through pandemic programs as regular state programs.

—Kim Mackrael contributed to this article.

Write to Eric Morath at eric.morath@wsj.com