More than 2.1 million Americans filed new unemployment claims last week, federal figures showed Thursday, as the 10-week total climbed to nearly 40.8 million since states shut down their economies to slow the spread of the coronavirus.

The weekly count of new claims in Pennsylvania, New Jersey, and the U.S. continued a downward trend after peaking in late March. But they remained at high levels more than two months after states restricted business operations and limited the movement of residents.

In total, 1.9 million Pennsylvania workers have submitted new jobless claims as of May 23, or 29% of the workforce, according to federal data. In New Jersey, 1.1 million workers have sought unemployment benefits, or 24% of the state’s workforce.

Initial weekly claims have steadily fallen since peaking at 6.9 million in late March, according to the U.S. Department of Labor. Still, the modest declines in recent weeks suggest that companies are still laying off workers at high levels, even as overwhelmed state unemployment offices continue to catch up on the backlog of applicants.

Even among the cascade of gloomy economic indicators, there were some encouraging signs. The number of workers receiving unemployment benefits, reported as continuing claims, fell from 25 million to 21 million during the week ending May 16 — a sign that reopening businesses are hiring workers who were on unemployment. Continuing claims figures lag a week behind initial claims filings.

Mark Zandi, chief economist at Moody’s Analytics, called Thursday’s report “dismal.” But he said there were “some green shoots in the data,” suggesting that the job market is close to turning the corner.

“Most encouraging is that continuing claims are now falling,” he said. “This means that while lots of workers are still losing their jobs, hiring is finally picking up, consistent with business reopenings across the country.”

With unemployment at historic levels not seen since the Great Depression, states have been under pressure to relax restrictions put in place to slow the spread of the coronavirus, which has infected more than 1.7 million Americans and killed more than 101,000.

Pennsylvania has put 49 of its 67 counties in the first, or “yellow,” phase of reduced restrictions, allowing retailers to operate at limited capacity and letting businesses call employees back to work if they can’t operate remotely. New Jersey has allowed retail stores with curbside delivery and nonessential construction to resume, along with outdoor businesses such as golf and shooting ranges.

In Pennsylvania, 69,408 workers filed new unemployment claims last week, up about 10% from the week before, while 33,290 workers filed for assistance in New Jersey, down 21% from the previous week, according to federal figures.

Pennsylvania saw another decline in continuing claims, shedding 95,618 to reach 913,268 as of May 16. In New Jersey, continuing claims fell 15,120 to 586,650.

On Wednesday, the Pennsylvania Department of Labor & Industry said it could not speculate what caused the state’s decrease in continuing claims for the week ending May 9. But a spokesperson said the decrease was most notable in the following industries: food services and drinking places; personal and laundry services; ambulatory health-care services; and social assistance.

The department said Tuesday that it crossed the $10 billion mark in unemployment benefits paid out to Pennsylvanians since March 15.

State officials also announced that the department’s anti-fraud division discovered attempts to bilk Pandemic Unemployment Assistance (PUA) benefits, a temporary federal program that provides financial help to those not eligible for regular unemployment compensation.

Labor & Industry Secretary Jerry Oleksiak declined to say how many fraudulent claims were filed or how much may have been stolen, citing an ongoing investigation. But he stressed that the personal information used to file the fraudulent claims was not stolen from the department.

“This is identity theft from before the COVID-19 virus,” he said. “The bad guys are using personal information they obtained without permission from other sources to file for PUA benefits and route those payments to their own bank accounts.”

To combat the fraud, the department will mail paper checks for PUA benefits to ensure that payments aren’t stolen, said Susan Dickinson, director of the state’s Office of Unemployment Compensation Benefits Policy. Anyone who receives a paper check in the mail and did not file for unemployment benefits in Pennsylvania should not cash or deposit it.

Even as fewer Americans are filing for new unemployment claims, some economists warned against reading that as a positive sign.

Joel Naroff, president and founder of Naroff Economic Advisors in Bucks County, said Thursday’s jobless report is likely to be viewed as good because it is the lowest level of new unemployment claims in nine weeks.

“But, really, is there any reason to see something positive in this level of claims? No,” he wrote in in a note to clients. “It signals that firms and governments are still massively cutting workers.”

Staff writer Chris A. Williams contributed to this article.