Both sides described the 90-minute meeting at the White House as useful and agreed to keep talking but no decision was made to resolve the 10-day deadlock over the federal budget.
The White House said it was a good meeting and that President Obama looked forward to progress after he held talks with 20 House Republicans, including Speaker John Boehner.
"After a discussion about potential paths forward, no specific determination was made. The President's goal remains to ensure we pay the bills we've incurred, reopen the government and get back to the business of growing the economy, creating jobs and strengthening the middle class," the White House said in a statement.
Earlier, the administration said Obama is ready to sign a bill approving a short-term debt ceiling, even without an agreement to end the shutdown.
"The president is happy that cooler heads at least seem to be prevailing in the House, that there at least seems to be a recognition that default is not an option," White House Press Secretary Jay Carney said on the move to raise the debt limit.
Both sides described the 90-minute meeting at the White House as useful.
Following the meeting, House Majority Leader Eric Cantor said that they had a "very useful" meeting with Obama and that they will continue to discuss the issue of debt ceiling and the government shutdown, which is now into its second week. "We had a very useful meeting.
It was clarifying I think for both sides as to where we are and the takeaway from the meeting was, our teams are going to be talking further tonight, we'll have more discussions," Cantor said. According to a Congressional aide, Obama neither said yes nor no to their proposal of a six-week debt ceiling hike.
Officials have warned the US risks a debt default on October 17 if the nation's borrowing limit is not increased. Republicans have offered to extend the government's borrowing authority beyond the deadline, temporarily putting off a default. In return they want Obama to further negotiate on the federal budget dispute that has partially closed the government - the first shutdown for 17 years.
A spokesman for Boehner said the deal offered was a "clean" increase of the debt limit, with no additional policies attached. It would only last six weeks - until November 22. But it is not clear if Republicans are willing to drop entirely their demands to defund or delay the president's contentious 'Obamacare' healthcare plan.