WASHINGTON — President Biden and Speaker Kevin McCarthy emerged from a critical meeting at the White House on Tuesday with no consensus on how to end their impasse over the federal debt and spending just weeks before the nation is set to default on its obligations for the first time in history.

With the American and perhaps the global economy hanging in the balance, the meeting was the first such session between the Democratic president and Republican speaker since February. But the two sides stuck close to their opening positions, with Mr. Biden demanding that Congress raise the debt ceiling unconditionally to avoid a default and Mr. McCarthy insisting that such a move be accompanied by serious spending restraints.

“We need to take the threat of default off the table,” Mr. Biden stressed after the meeting in a news conference. He described the discussion as productive and said that he and congressional leaders would meet again Friday.

“Everyone in the meeting understood the risk of default,” he said.

But his chief rival in the discussion was unsatisfied with the meeting. “I didn’t see any new movement,” Speaker Kevin McCarthy told reporters. He said he asked Mr. Biden “numerous times” if there were places in the federal budget they could find “savings” — meaning cuts. “They wouldn’t give me any,” he said. That is consistent with what the White House has publicly said: Mr. Biden would not tie any cuts to raising the debt limit.

Senator Mitch McConnell, the minority leader, insisted that the United States would not default. “What we have here, is we’re running out of time,” Mr. McConnell said. Mr. McCarthy has suggested that a deal should be hammered out in the next two weeks to leave enough time for legislation to be passed.

For the Democrats, Senator Chuck Schumer, the majority leader, said that in the meeting, Mr. McCarthy refused to promise that the United States government would not default.

“There are probably some places we can agree, some places we can compromise,” Mr. Schumer said about federal spending. But that has to occur separately, not as part of debt ceiling negotiations, he said, maintaining the White House line.

Here’s what else to know:

• The leaders will meet again on Friday. In recent years, such standoffs have not been resolved until hours or days before a deadline — or the deadline is extended.

• Mr. Biden suggested he might miss the Group of 7 leaders meeting in Japan next week in order to resolve the debt limit. “It is possible,” he told reporters.