However, officials took the opportunity to further indicate they do not expect the United States will default on its debt obligations early June, the deadline earlier given by the US Treasury Department.
"I didn't see any new movement," US House Speaker Kevin McCarthy said. "I would hope that he would be willing to negotiate for the next two weeks so we could actually solve this problem and not take America on the brink."
US Senate Minority Leader Mitch McConnell, who was also in attendance at the highly-anticipated meeting, told reporters the United States would by no means default on its debt obligations.
"The United States is not going to default. It never has, it never will," he said. "However, elections have consequences. We now have divided government."
Moments after the Republican leadership held a presser, US House Minority Leader Hakeem Jeffries remarked in a separate conference that Biden asked congressional leaders to meet as soon as Tuesday evening to resume negotiations on raising the debt ceiling.
"President Biden has asked the four corners of the Capitol along with the administration to get together as early as this evening, if not tomorrow, to make sure that we can have a conversation about the budget, about the appropriations process, about spending and investments and revenue - and all four parties have agreed," Jeffries told reporters.
McCarthy had earlier indicated that he expected staffers to assemble for another round of negotiations on Friday. Biden in his own follow-up news conference confirmed he would be meeting with congressional leadership on Friday.
Echoing comments made by McConnell, Biden told press that a US default was "not an option." He also stated he was prepared to hold separate talks on budget and spending priorities - but not under the threat of default.
Biden also reiterated that he has been "considering the Fourteenth Amendment," but that it would have to be litigated in court.
However, the Obama White House never pursued the 14th Amendment route, with former White House spokesperson Jay Carney saying in 2012 the administration determined the president lacks such authority.
Aside from McCarthy, McConnell and Jeffries, Biden had also been joined in the Oval Office by Senate Majority Leader Chuck Schumer.
Since January, the US has been operating under "extraordinary measures" after the US hit its $31.4 trillion debt limit. US Treasury Secretary Janet Yellen has stated that its temporary fix may run out as early as June 1.