New applications for unemployment benefits held near pandemic lows last week while the number of Americans collecting continuing payments fell sharply in late June as many states acted to curtail jobless aid.

Initial unemployment claims, a proxy for layoffs, rose by 2,000 the week ended July 3, from a pandemic low the prior week, to a seasonally adjusted 373,000, the Labor Department said Thursday. The four-week moving average, which smooths out volatility in the weekly figures, was 394,500, the lowest reading since March 2020.

Meanwhile, the number of continuing unemployment payments made through regular state programs fell by 145,000 to the lowest level since March 2020, for the week ended June 26.

Unemployment assistance payments made through pandemic programs fell by nearly a half million for the week ended June 19 as some states ended their participation last month. Continuing claims data is reported on a delay.

“Economic recovery and the associated suspension of supplemental unemployment benefits could incentivize people to take jobs, making the jobless numbers fall further,” said Jason Schenker, president of Prestige Economics.

About half of states have announced that they will cut off enhanced and extended unemployment benefits before they are slated to end nationwide in early September. Alaska, Iowa, Missouri and Mississippi were the first to cut off payments as of June 12. Another 18 states were set to cut off payments by the end of June and four more this month, though some are facing legal challenges around those plans.

Tim Dillard, owner of an Express Employment Professionals franchise in Flowood, Miss., said he noticed a significant change at the staffing firm after Gov. Tate Reeves, a Republican, announced the end of enhanced unemployment benefits in mid-May.

“It’s almost like someone turned the faucet on,” Mr. Dillard said. “Companies are hiring—we still have more orders than workers to fill them—but people are starting to come in more.”

In the past six months, the Express office would often have 75% of those scheduled for interviews not show up, but the no-show rate fell to less than 50% after the announcement, he said.

Mr. Dillard said the end of benefits was an important factor, but not the only one drawing workers back. He said wages for entry-level industrial jobs, such as machine operators, are up 25% from 18 months ago, and wages for administrative jobs are up more than 10%. He said the removal of all Covid-19 restrictions in the state has sent the signal that the pandemic is coming to an end, encouraging some people to restart job searches.

Low-wage work is in high demand, and employers are now competing for applicants, offering incentives ranging from sign-on bonuses to free food. But with many still unemployed, are these offers working? Photo: Bloomberg The Wall Street Journal Interactive Edition

Thursday’s report showed Mississippi didn’t make any pandemic-related payments in the June 19 week, and several others, such as Missouri and Texas, appeared to be winding down programs, paying tens of thousands of fewer continuing pandemic claims than the prior week. However, pandemic payments also fell in states such as California and Illinois, which are slated to maintain benefits until September.

Continuing claims paid through the two pandemic programs fell to 10.7 million for the week ended June 19, the Labor Department said. That was the lowest level since early January. Data for pandemic programs isn’t seasonally adjusted.

Congress last year approved two emergency unemployment programs to respond to the pandemic. One made payments available to the self-employed, gig workers and others typically not eligible for benefits. The other allowed those who exhaust other programs, which typically last six months or less, to continue to receive payments. Those on any type of unemployment benefit have also received a $300 weekly enhancement on top of other payments since late December.

Eligibility for regular state benefits isn’t affected by states’ withdrawal from federal pandemic programs, but unemployment recipients won’t receive the $300-a-week enhancement to state payments if they live in a state that has canceled that bonus or will soon do so. Economists from Goldman Sachs found the number of continued payments for regular state programs have fallen more swiftly since April in states planning to remove the enhancement.

The general downward trend in both initial and continuing jobless claims in recent months came as hiring accelerated in May and June and infection rates have declined with the widespread availability of Covid-19 vaccines.

“Employment is still on a strong upward trajectory,” said Gregory Daco, chief U.S. economist at Oxford Economics. “Demand for labor is very strong,” and impediments to returning to work are easing, he said. In addition to unemployment benefits, Mr. Daco said lack of child care and fear of contracting the virus are lingering, which explains why some people are reluctant to return to jobs, although those concerns are fading.

A separate Labor Department report Wednesday showed that there were more than nine million unfilled jobs at the end of May, the highest level in records back to 2000.

Still, some unemployed workers say they are still struggling to find jobs. Marcellus Rowe of Dunwoody, Ga., said he has been unable to find a job that pays a salary near the roughly $50,000 he made working for the Metropolitan Atlanta Rapid Transit Authority. Mr. Rowe, 29 years old, lost that job in November 2019, before the pandemic, but was able to stay on unemployment benefits because of the federal extensions. Georgia cut off those benefits late last month.

Mr. Rowe said he has applied for more than 100 jobs, including security-guard and customer-service roles. He said the few employers who have responded to him said he doesn’t have the experience needed for the positions. Mr. Rowe, a Black man, added that he thinks his race is a reason he has been passed over for some jobs.

He said he is reluctant to take a minimum-wage job because $7.25 an hour wouldn’t be enough to pay his rent and other bills. He sought housing assistance from his county when benefits expired.

“The job market isn’t looking so great,” he said. “I’m looking for suitable jobs, but it’s not happening here in Georgia.”

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