Mainers continue to file new claims for unemployment assistance, even as the state has allowed most businesses to reopen to the public.

Another 4,100 workers filed initial unemployment insurance claims last week, the Maine Department of Labor reported. That number was down slightly from about 4,500 the week before.

About 3,000 claims were filed for state unemployment benefits and another 2,200 claims for federal assistance, for a total of 5,200 claims. The department typically records more claims than individual claimants because of significant overlap between state and federal benefits programs. A week earlier, the total number of state and federal claims filed in Maine was 5,600, which included 1,100 duplicate claims caused by overlap between the two systems.

While the numbers of new unemployment claims have fallen considerably from the height of mass layoffs in late March and April, thousands of Mainers continue to file new claims every week, pointing to the depth of the economic recession hitting the state and country.

Roughly 62,300 weekly claims were filed for continued state assistance and 28,000 claims for continued federal assistance last week. Those numbers were down slightly from the previous week.

Maine’s unemployment system also has been beset by widespread fraud allegedly perpetrated by organized criminal groups using stolen personal information. Another ongoing issue is a delay in adjusting benefits for self-employed and contract workers from the state’s minimum weekly allotment of $172 to a figure based on each claimant’s prior income. The state initially said it would have those adjustments made by June, but then its staff became mired in a prolonged investigation into fraudulent claims.

While the state has cracked down on fraud by reinstating thorough vetting for new unemployment claims, continued fraud could inflate claims data. State investigators canceled 720 initial claims and 3,000 continuing claims suspected of being fraudulent last week, the department reported.

Some of the recently canceled claims were filed last week and some were filed earlier, said Labor Department spokeswoman Jessica Picard.

“Fraudulent claims continue to be filed each week, and the department continues to refine the flagging system for potential fraud in order to continue catching these false claims while reducing disruption to legitimate claimants,” she said.

The department and state and federal law enforcement agencies are still investigating how much money in benefits may have been lost to fraud and the organizations allegedly responsible, Picard added.

Overall, about 24,600 initial claims and 44,000 weekly claims have been canceled for being fraudulent since late May, when state authorities recognized the scale of the problem.

This week, Gov. Janet Mills’ administration moved into the third stage of the state’s economic reopening, allowing movie theaters, amusement parks, performing arts venues, spas and other businesses to reopen with restrictions. The vast majority of businesses are allowed to serve customers now, but the pace and scale of economic recovery is uncertain.

The state’s projected unemployment rate in May was 9.3 percent, but state economists said the true rate is likely 18 percent after correcting for inaccurate survey data.

The U.S. added an estimated 4.8 million jobs last week, but reclosings of businesses as COVID-19 cases surge in some parts of the country are keeping layoffs elevated.

The number of Americans who sought unemployment benefits barely fell last week to 1.47 million. Though that weekly figure has declined steadily since peaking in late March, it’s still more than double the pre-pandemic peak set in 1982. And the total number of people receiving jobless aid remains at a sizable 19 million.

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