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Updated at 11:30 a.m. ET

Republican senators and the White House have reached an agreement on major elements of an upcoming coronavirus aid bill but have yet to settle on how to address unemployment benefits set to expire at the end of this month.

The agreement, which includes $105 billion for schools and $16 billion for testing, is meant to be a starting point for bipartisan talks on a final bill. The full package was expected Thursday morning, but haggling over unemployment stalled the release.

Treasury Secretary Steven Mnuchin and White House Chief of Staff Mark Meadows returned to Capitol Hill on Thursday morning for further talks.

Mnuchin said they are focused on a new federal unemployment benefit that would replace roughly 70% of the wages a person was previously earning.

"I think we are very clear on we're not going to pay people more to stay home than to work," Mnuchin told reporters at the White House. "So we're looking at something that looks like a 70% wage replacement, and we're working on the mechanics of that."

Those mechanics have been a major hurdle in the unemployment talks. Lawmakers settled on the $600 in weekly benefits that are currently available because they could not coordinate state systems quickly enough. Democrats and Republicans said at the time that they would have liked to tailor unemployment benefits more closely to what people made when they were working.

Top congressional Democrats criticized the GOP for failing to support jobless Americans and dismissed the idea of working on some kind of temporary extension for unemployment aid while a broader bill was being negotiated.

"We cannot piecemeal this," House Speaker Nancy Pelosi, D-Calif., told reporters at her weekly press conference, adding, "I go to the table with a commitment for the $600."

The Senate GOP agreement does not include the payroll tax cut President Trump had been pushing.

Republican members of the Senate Appropriations Committee announced a separate portion of the agreement Wednesday night. The senators said the legislation, which will be released in full Thursday, meets their priorities of getting people "back to school, back to child care and back to working."

The school funding includes $30 billion for colleges and universities, $70 billion for K-12 education and $5 billion for governors to allocate as needed.

"There will be some money distributed to all districts," said Sen. Roy Blunt, R-Mo. "And other money that will be distributed to districts that get back to school in a more traditional sense."

Half of the money for K-12 schools would go to all schools on a per-capita basis; the other half would be distributed to schools that go back to a traditional school setting rather than using distance learning.

The senators also described funding for testing for nursing homes, child care facilities and schools, though exact figures were not released.

Blunt described a scenario in which the legislation could be broken down into several separate bills rather than one large package, as has been the practice for previous relief legislation.

The senators did not provide details of how Republicans plan to handle unemployment insurance or direct payments to individuals, all elements that are being finalized by other committees.

Democrats passed their version of the next round of coronavirus relief more than two months ago. But Republicans have struggled to unite over whether more aid was necessary as well as key benefits such as unemployment insurance, direct payments and the total cost.

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