More than 3,000 migrants poured into the Big Apple in just the last week alone — a sign the surge of asylum seekers isn’t slowing down, officials said Wednesday.

The latest figures came as City Hall faced off against Gov. Hochul in a Manhattan courtroom Wednesday to push Albany to provide new sites for housing and billions in aid to help cover the estimated $12 billion price tag.

“Unless we are able to get sustained and coordinated state and federal support, work authorization and a decompression strategy will be forced to be playing this whack-a-mole racing to keep opening relief centers as asylum seekers keep arriving by the thousands,” Deputy Mayor for Health and Human Services Anne Williams-Isom said during a press briefing.

“It’s simply unsustainable.”

As of Sunday, the city had 59,300 migrants in its care across 206 sites — including 15 mega-shelters run by the public hospitals corporation.

Just last week, between Aug. 14 and 20, another 3,100 new asylum seekers arrived in the Big Apple, bringing the tally to 104,400 since last spring.

Williams-Isom said progress has been made but the city cannot keep up with the influx unless it receives more funding from the state and federal government.

She highlighted the hundreds of single migrants who have been moved to the state-supported sites at Creedmoor in Queens and on Randall’s Island, roughly 800 and 350 adults, respectively.

City officials also lauded the tentative deal struck between Hochul and the feds that could turn Floyd Bennett Field into an emergency shelter site as an important “movement,” but said that getting the site up and running is still weeks away.

“We’re still working out the details with the federal and state governments, but we’re grateful to Governor Hochul for her partnership in advocating for this site and for her commitment to helping to pay for it,” Williams-Isom said.

Ted Long, a top official with the city’s hospital system, reiterated the administration’s longstanding position that Albany has also been hammering home to the White House.

“They need to be authorized to work so that they can work quickly to make the money that they need to protect and be reunited with their families,” he said.

“That’s why at this point in the crisis, as the deputy mayor said, and as the mayor has said, we need help.”