The White House offered a new COVID-19 relief package worth $916 billion to House Speaker Nancy Pelosi, Treasury Secretary Steven Mnuchin said on Tuesday.

Mnuchin noted that the new stimulus package includes money for state and local governments, the Business Insider reported. He also said there would be liability protection for businesses, schools, and universities.

Mnuchin did not cite any new stimulus checks, but House Minority Leader Kevin McCarthy said the proposal would send a $600 direct payment to Americans.

The new White House proposal is slightly higher than the $908 billion aid proposal being crafted by a bipartisan group of moderate senators. Mnuchin said he had discussed the package in a phone conversation with Pelosi on Tuesday afternoon.

According to Pelosi and Senate Minority Chuck Schumer, the proposal would cut unemployment insurance spending to $40 billion from $180 billion in the bipartisan framework, and said this is "unacceptable."

"While it is progress that (Senate Majority) Leader (Mitch) McConnell has signed off on a $916 billion offer that is based off of the bipartisan framework, the President's proposal must not be allowed to obstruct the bipartisan Congressional talks that are underway," Pelosi and Schumer said in a Business Insider report.

But for McCarthy, he said the White House's proposal with $600 direct payments and an additional $600 per child is much better.

Democrats and Republicans are trying to ramp up their calls for direct payments in the next aid package. 

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A White House spokesperson said that while the amount is yet to be determined, direct payments to American workers continue to be a top priority of President Donald Trump.

The White House proposal did not contain any extra federal unemployment benefits.

Trump earlier authorized a $300 federal benefit for unemployed workers in the summer through an executive order. The program lasted only six weeks.

McConnell had earlier proposed shelving aid to state and local governments. However, Democrats rejected McConnell's proposal, saying that not aiding state and local governments could accelerate layoffs among firefighters, police officials, and other public workers.

Democrats have been prioritizing providing assistance to them. Schumer said that state and local funding is bipartisan, further accusing McConnell of attempting to sabotage the talks.

Sen. Susan Collins said that as of now, they are targeting struggling families, failing businesses, health care workers, adding that they do not have a stimulus check for every single person, the Associated Press reported.

McConnell said Congress would not leave without a stimulus relief package that has been long overdue. 

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The Kentucky lawmaker said he would not propose a relief bill that does not cover a liability shield being sought by businesses, universities, nonprofits, and other reopening facilities during the pandemic.

Pelosi earlier demanded more than $900 billion for state and local governments this spring. Meanwhile, Capitol Hill officials are moving a government shutdown deadline to the end of next week.

The House and Senate are set to vote a one-week spending bill on Wednesday to keep the government open until December 18 and buy more time for stimulus negotiations.