By Eric Morath

New applications for unemployment benefits held nearly steady last week after a period of larger declines, a sign an increased number of Covid-19 cases in some states and related restrictions on businesses is causing the labor market's healing to stall.

Initial unemployment claims fell by a seasonally adjusted 10,000 to 1.3 million for the week ended July 11, the Labor Department reported Thursday.

That narrowly extends a trend of declines from a peak of 6.9 million in late March, when the coronavirus pandemic and mandated business closures shut down swaths of the U.S. economy. Last week's level was well above the highest week on record before this year, which was 695,000 in 1982.

The number of Americans receiving unemployment benefits fell by 422,000 to 17.3 million for the week ended July 4, the lowest reading since the week ended April 11. Those so-called continuing claims are reported with a week lag.

The modest easing of the number of unemployment rolls suggests new layoffs are being offset by hiring and recalling of workers. Employers added a combined 7.5 million jobs in May and June after shedding 21 million jobs in March and April, separate Labor Department data showed.

Claims data were mixed across states. Applications for benefits rose significantly in Florida, and also increased in Georgia and California. They fell in Texas, New Jersey and Michigan.

In addition to regular state programs that cover about 90% of U.S. workers, unemployment benefits have been expanded to those who were previously ineligible for such aid, including self-employed and gig-economy workers. Others who are now potentially eligible include those who can't work because they're ill with Covid-19 or caring for someone who is ill, those who don't have available childcare and those who had a job offer rescinded due to the pandemic.

Last week, 928,000 sought new benefits through that program, which is accounted for separately from the regular unemployment insurance program and not adjusted for seasonality. For the week ended June 27, the latest available data, the number receiving payments through the program rose by 406,000 to 14.3 million.

The number tapping benefits through the Pandemic Unemployment Assistance program now nearly matches the number in the state programs,according to the state data reported to the Labor Department. However, economists caution that accounting for the new program is inconsistent across states. A Labor Department spokeswoman said Wednesday the department doesn't have a count of individuals receiving the pandemic assistance.

The Century Foundation, a left-leaving think tank, estimates the total number receiving unemployment benefits is about 25 million.

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