BATON ROUGE, La. (AP) — Louisiana should start issuing checks for $300 in weekly federal coronavirus unemployment aid next week, but as many as 87,000 people receiving state unemployment may not be eligible for the federal assistance, Gov. John Bel Edwards said Tuesday.

The state expects to receive $375 million in federal funds by the end of this week to start paying out the enhanced federal unemployment benefits offered by President Donald Trump's executive order, Edwards said. Louisiana is working on changes to its unemployment computer system to process those payments.

“Next week is when we believe that we will be issuing these checks,” the Democratic governor said.

About 417,000 people will get the federal unemployment aid, with the Edwards administration saying people will receive three weeks of payments at once, because the assistance is retroactive to Aug. 1. The money comes on top of weekly state unemployment benefits, which max out at $247.

But not everyone receiving state unemployment will get the federal aid.

Edwards said 67,000 people receive too little in state unemployment to qualify for the federal benefits, while another 20,000 currently receiving state unemployment assistance not tied to the coronavirus outbreak won't be eligible unless they can show their job losses are linked to the pandemic.

Congress approved $600 weekly federal unemployment payments, on top of what states pay in unemployment assistance, but that enhanced benefit expired at the end of July.

Trump’s executive order takes $44 billion from a Federal Emergency Management Agency disaster relief fund and offers states additional unemployment payments using that money. Critics question the validity of the order. And it's unclear how long that unemployment assistance will last before the federal disaster relief dollars run out.

Louisiana continues to have one of the nation’s highest per capita virus infection rates in recent weeks. But the average number of new confirmed cases per day has fallen by about 40% over the past 14 days, to about 1,000.

“We are seeing modest and sustained improvement in our numbers,” Edwards said. “The case growth rate is still an indication that we have a lot of work to do and that everybody needs to play their part” in wearing masks and staying distanced from others.

For most people, the coronavirus causes mild or moderate symptoms. For some, especially older adults and those with existing health problems, it can cause more severe or fatal illness.

More than 139,000 cases of the coronavirus have been confirmed by Louisiana’s health department, though the true number of virus infections is thought to be far higher because many people have not been tested and studies suggest people can be infected without feeling sick. The state's death toll from the COVID-19 disease caused by the coronavirus grew by 28 Tuesday, reaching 4,431.

The health department says more than 103,000 people in Louisiana have recovered.

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Follow AP coverage of the pandemic at https://apnews.com/VirusOutbreak and https://apnews.com/UnderstandingtheOutbreak.