WASHINGTON—The federal government will this week release funds from a coronavirus stimulus package to boost jobless benefits, but how quickly those payments reach laid-off workers depends on overburdened state unemployment systems, the head of the U.S. Labor Department said in an interview.

A record-shattering 3.3 million Americans applied for unemployment benefits two weeks ago as a result of U.S. shutdowns due to the coronavirus pandemic. Economists forecast weekly data to be released Thursday will show another 3.1 million sought assistance last week. The recent levels of people seeking jobless claims are more than four-times previous records, causing delays in applications and putting pressure on state benefit systems.

Laid-off workers have reported waiting on the phone for hours and websites crashing, leaving them unable to apply. Those who do successfully file are waiting for the additional $600 a week in jobless payments, approved by Congress and President Trump last week.

“What we’re focused on now is making the system that we have in place function as effectively as possible,” Labor Secretary Eugene Scalia said.

He said funds to increase jobless payments by $600 a week—more than double the existing maximum in some states—will be distributed to states this week, but he doesn’t know when states will make such payments to individuals. The enhanced benefits were included in the roughly $2 trillion stimulus package that was recently signed into law.