US President Joe Biden and top Republican Kevin McCarthy have called their latest talks on the debt ceiling productive but no deal has yet been reached, reports BBC.
"I believe we can get a deal done," House Speaker McCarthy told reporters.
While acknowledging areas of disagreement, Mr Biden said "default is off the table".
Treasury Secretary Janet Yellen has reiterated that the US will likely default on its debt as early as 1 June.
The debt ceiling is a spending limit set by Congress which determines how much money the government can borrow.
Failure to raise it beyond the current cap of roughly $31.4tn (£25.2tn) by June could result in the US defaulting on its debt.
That would mean the government could not borrow any more money or pay all of its bills. It would also threaten to wreak havoc on the global economy, affecting prices and mortgage rates in other countries.
The president ended his trip to Japan for the G7 summit early and returned to the US on Sunday to address the deadlock over US debt.
In a statement issued after his meeting with the House speaker, Mr Biden said: "Default is off the table, and the only way to move forward is in good faith toward a bipartisan agreement."
The tone of the talks at the White House appeared to be more optimistic after weeks of divisive partisan discourse. But it is unclear how quickly the two sides can reach a deal.
"We don't have an agreement yet," Mr McCarthy said. "But I did feel the discussion was productive in areas that we have differences of opinion.''
"Biden and I will talk everyday until we get this done," he said.
Mr McCarthy said the source of the stalemate between Democrats and Republicans is the same as it has always been, spending.
But while recognising the differences he said the tone "was better than at any other time".
Earlier, the House speaker emphasised that a deal needed to be reached this week to give Congress adequate time to meet the 1 June deadline.
He estimated it would take about 72 hours for the agreement to be written, read and voted on.
Treasury Secretary Janet Yellen issued a warning letter to Congress on Monday maintaining that the US would likely run out of money to pay its bills as early as 1 June without a debt limit increase.
She heightened the urgency and called the possibility of a default in early June "highly likely".
"If Congress fails to increase the debt limit, it would cause severe hardship to American families," her statement read.
Republicans are demanding over $4tn in budget cuts which would dissolve several of Mr Biden's legislative priorities.
Democrats have refused and instead are offering to keep spending flat.
Both Mr Biden and Mr McCarthy are under pressure from the left and right flanks of their respective parties to hold the line.
With a one-seat Democratic majority in the Senate and Republicans in narrow control of the House, a deal has so far proven elusive.