US President Joe Biden and top Republican Kevin McCarthy have described their latest talks on the debt ceiling as fruitful, but no deal has yet been reached.
“I believe we can make a deal,” House Speaker McCarthy told reporters.
Acknowledging areas of disagreement, Mr Biden said “default is off the table”.
Treasury Secretary Janet Yellen has reiterated that the US will default on its debt as early as June 1.
The debt ceiling is a spending limit set by Congress that determines how much money the government can borrow.
Failure to raise it beyond the current limit of around $31.4tn (£25.2tn) by June could result in the US defaulting on its debt.
This would mean that the government could no longer borrow money or pay all its bills. It would also threaten to destabilize the global economy, affecting prices and mortgage rates in other countries.
The president ended a trip to Japan early for the G7 summit and returned to the US on Sunday to address the US debt impasse.
In a statement issued after his meeting with the House Speaker, Mr Biden said: “Default is off the table, and the only way forward is in good faith towards a bipartisan agreement.”
The tone of the talks at the White House appeared more optimistic after weeks of divisive partisan talk. But it is unclear how quickly the two sides can reach an agreement.
“We don’t have a contract yet,” Mr McCarthy said. “But I felt that the discussion was productive in areas where we disagreed.”
“Biden and I will talk every day until we get this done,” he said.
Mr. McCarthy said the source of the deadlock between Democrats and Republicans is what it always has been, spending.
But while acknowledging the differences, he said the tone was “better than ever”.
Earlier, the House speaker stressed that a deal needed to be reached this week to give Congress enough time to meet the June 1 deadline.
He estimated it would take about 72 hours to write, read and vote on the agreement.
Treasury Secretary Janet Yellen issued a warning letter to Congress on Monday saying that without raising the debt ceiling, the United States will run out of money to pay its bills by June 1.
He added urgency and called the possibility of a default “highly likely” in early June.
“If Congress fails to raise the debt ceiling, it will put American families in dire straits,” his statement read.
Republicans are calling for more than $4tn in budget cuts that would eliminate many of Mr Biden’s legislative priorities.
Democrats have refused and are instead offering to keep spending flat.
Both Mr. Biden and Mr. McCarthy are under pressure from the left and right of their respective parties.
With a one-seat Democratic majority in the Senate and Republicans in narrow control of the House, a deal has so far proved elusive.
