But the Republican House of Representatives Speaker Kevin McCarthy told reporters the two sides are still far apart, the BBC reported.
The standoff has forced Biden to cut short a foreign trip.
Without a deal, the US could enter a calamitous default on its $31.4 trillion debt as soon as June 1.
A failure by the government to meet its debt obligations could trigger global financial chaos, the BBC reported.
The President said Tuesday’s hour-long Oval Office meeting was “good, productive”, sounding upbeat about the prospects of an agreement.
McCarthy said afterwards he believed a deal was possible by the end of this week.
Asked about the risk of the US falling off a fiscal cliff, the California Congressman told the BBC: “The great thing about that question is we’ve already taken default off the table.”
The House Speaker also told reporters a Biden-appointed representative would negotiate directly with his staff, which he said was a sign that “the structure of how we negotiate has improved.
The President is due to fly to the G7 summit in Japan on Wednesday.
He was then expected to head to Papua New Guinea and Australia for further meetings.
But he will now return after the May 19-21 summit ends in Hiroshima to “ensure that Congress takes action” to avert a default, the White House said in a statement.
The so-called Quad meeting in Sydney has now been cancelled, and the leaders will attempt to meet on the sidelines of the G7, Australian Prime Minister Anthony Albanese said. (IANS)
