REHOBOTH BEACH, Del. — President Joe Biden and congressional leaders will likely resume talks on Tuesday at the White House over the debt limit, the president said Sunday, as the nation continues to edge closer to its legal borrowing authority with no agreement in sight.

The meeting was initially supposed to be Friday, but was abruptly postponed so staff-level talks could continue before Biden and the four congressional leaders huddled for a second time. Administration and congressional officials said Sunday that a meeting has not been finalized, although Tuesday was the likeliest option as Biden returns to Washington on Monday and is scheduled to leave for the Group of 7 summit in Japan on Wednesday.

Biden did not detail much progress in the talks, but said he remained hopeful that an agreement could be reached with Republicans to avoid what would be an unprecedented debt default, which could trigger a financial catastrophe.

“I remain optimistic because I’m a congenital optimist,” Biden told reporters while out for a bike ride in Rehoboth Beach, Delaware. “But I really think there’s a desire on their part as well as ours to reach an agreement. I think we’ll be able to do it.”

Aides said talks had continued throughout the weekend. Biden has called on lawmakers to lift the debt limit without preconditions, warning that the nation’s borrowing authority should not be used to impose deep spending cuts and other conservative policy demands.

“We’ve not reached the crunch point yet,” Biden told reporters Saturday. “There’s real discussion about some changes we all could make. We’re not there yet.”

The president described last Tuesday’s Oval Office session with House Speaker Kevin McCarthy, R-Calif., House Democratic leader Hakeem Jeffries of New York, Senate Majority Leader Chuck Schumer of New York and Senate Republican leader Mitch McConnell of Kentucky — as “productive.”

McCarthy said later he “didn’t see any new movement” toward resolving the stalemate. White House and congressional aides have been in talks since Wednesday.

“The staff is very engaged. I would characterize the engagement as serious, as constructive,” Lael Brainard, head of the White House’s National Economic Council, said on CBS’ “Face the Nation.”