No specific agreement was reached, although a White House spokesman said the President "looks forward to continued progress with members on both sides".
In statements afterward that struck the most positive tone in weeks of acrimony, House Republicans described their hour-and-a-half-long meeting with Mr. Obama as "a useful and productive conversation,” while the White House described "a good meeting,” though "no specific determination was made” about the Republicans’ offer. Both agreed to continue talks through the night.
People familiar with the meeting said that Mr. Obama pressed Republicans to reopen the government, and that Republicans raised the possibility that financing could be restored by early next week if terms for broad budget negotiations could be reached.
The talks came after Mr. Boehner proposed a six-week extension to the US debt ceiling in return for the President's promise to negotiate over budget issues including the health care plan dubbed Obamacare.
The president "didn’t say yes, didn’t say no,” said Representative Paul D. Ryan, Republican of Wisconsin and chairman of the House Budget Committee. He added, "We agreed to continue talking and continue negotiating.”
Senate Democrats had their own White House meeting with Mr. Obama and Vice President Joseph R. Biden Jr. three hours before the House Republicans arrived, and the majority leader, Senator Harry Reid of Nevada, declined to embrace the Republicans’ debt limit proposal until he saw it.
The president has insisted he will not agree to significant reductions in projected Medicare and Medicaid spending — even his own tentative proposals — unless Republicans agree to raise revenues by curbing tax breaks for corporations and wealthy individuals. And Mr. Boehner in recent days reaffirmed the party’s anti-tax stance, which suggests that future talks could founder.
US Republican Representative Pete Sessions on Thursday said that he was hopeful House of Representatives Republicans and the Obama administration can strike a deal by Friday on legislation raising the US debt limit and funding the federal government.
Sessions, chairman of the powerful House Rules Committee, said that over the next 15 hours or so, the White House and House Republicans will work on "defining parameters to see if we can make progress."
If that progress is achieved, the two sides would then try to complete a deal, possibly on Friday.
Negotiations over raising the US debt limit - even on a temporary basis - remained up in the air late Thursday after the country's top Republican leader rushed out of a meeting at the White House with President Barack Obama without commenting.
The White House issued a statement calling it a "good meeting." The statement said Obama, a Democrat, looked forward to making continued progress with both Republicans and Democrats.
President Barack Obama and congressional Republicans found no specific way forward to break their impasse over a government shutdown and extending the US debt ceiling at a meeting on Thursday, the White House said.
The session of about an hour and a half between Obama and Republican leaders of the House of Representatives was described as a good meeting where Obama heard House Speaker John Boehner explain Republican proposals for a short-term extension of the US debt ceiling.
"After a discussion about potential paths forward, no specific determination was made," said a White House statement. "The president looks forward to making continued progress with members on both sides of the aisle."
Earlier Representative Paul Ryan told reporters that President Barack Obama neither accepted nor rejected a short-term debt ceiling proposal floated by US House of Representatives Republicans .
Other Republican leaders, including House Majority Leader Eric Cantor, said that House and Obama administration teams will continue working late on Thursday on the fiscal crisis.
"Hopefully, we will have a clearer path forward," Cantor, flanked by fellow House Republican leaders, told reporters on his return to the Capitol from the White House.
Representative Cathy McMorris Rogers, a member of the top Republican leadership in the House of Representatives, gave the details of the Republican proposal at a press conference.
She said the Republican leadership would offer legislation that "will offer a temporary increase in the debt ceiling to allow us some time, because it is time for solutions."
The talks at the White House occurred late Thursday after Obama invited the entire Republican membership in the House - 232 members - but Boehner rejected the offer.
Obama has repeatedly declared his willingness to negotiate with Republicans - but only after the House passes a clean bill to raise the debt ceiling and another bill to end the 10-day closure of the US government.
The US government will reach its borrowing limit on or about October 17, at which time it would have to default on bond payments held by international and domestic investors. Many entitlements such as medical care for the poor and aged and social security would suffer, the administration has said.
Spokesman Jay Carney said Obama was happy that "cooler heads" seem to be prevailing, but that the president believes it would be better to raise the debt ceiling for an "extended period of time" rather than a short period.
In addition to a debt ceiling agreement, Obama wants the hardline Republicans to pass a budget so the government can end its partial shutdown.
"They gotta turn on the lights and let us pay our bills," Carney said.
The prospect of default has raised alarm in the world's financial system, and triggered warnings of recession from the heads of major international organizations.
But on Thursday investors breathed a sigh of relief and the Standard & Poor's 500 Index rallied 1.7 per cent and the Dow Jones Industrial Average gained 1.6 per cent - the biggest jump since January, according to Bloomberg news agency.
Angel Gurria, the head of the Paris-based Organization for Economic Cooperation and Development (OECD), earlier Thursday said if the debt ceiling is not raised, its calculations suggest that the OECD region as a whole would be pushed back into recession next year and emerging economies would experience a sharp slowdown.
World Bank President Jim Yong Kim said a default - even a "near miss" - would be particularly harmful to developing countries. An August 2011 debt crisis, in which the limit was raised only in the final hours, was a "near miss" that roiled stock and credit markets and made it more expensive for poor countries to borrow.
Treasury Secretary Jacob Lew warned a Senate hearing that "irrevocable damage" would result if the federal government defaults on is obligations for the first time in history. He said it would be "deeply damaging" to financial markets and undermine already sluggish US economic recovery.
President Barack Obama is willing to sign a "clean" bill to raise the US debt ceiling - one that does not include policy demands - but it is not yet clear what House Republicans are proposing, White House spokesman Jay Carney told reporters on Thursday.
"The president is happy that cooler heads at least seem to be prevailing in the House," Carney said, responding to news on Thursday that House Republicans are working on a short-term extension of the debt ceiling.
"We haven't seen a bill yet," Carney said.
President Barack Obama is willing to look at a proposal by congressional Republicans to extend the debt ceiling for six weeks but insists that lawmakers end the 10-day government shutdown as well, a White House official said on Thursday.
The White House did not reject outright, but reacted cautiously, to a plan that House of Representatives Speaker John Boehner presented to fellow House Republicans ahead of a meeting they were to hold with Obama on Thursday.
The official, speaking on condition of anonymity, insisted Obama would not agree to negotiations over the debt limit, a primary goal of conservative House Republicans.
"While we are willing to look at any proposal Congress puts forward to end these manufactured crises, we will not allow a faction of the Republicans in the House to hold the economy hostage to its extraneous and extreme political demands," the official said. "Congress needs to pass a clean debt limit increase and a funding bill to reopen the government."
Republican members of the US House of Representatives expressed concern on Thursday that President Barack Obama will refuse to negotiate on fiscal issues even if they approve a six-week debt limit hike without conditions, senior Republican aides said.
"There is a lot concern from members from all sides" about the emerging proposal for a short-term increase in the debt limit, one senior aide said. The US Treasury expects to exhaust its remaining borrowing capacity by October 17.
Representative Rodney Davis, a moderate Republican from Illinois, said he believed that despite the concerns, House Republicans will back the short-term debt limit increase plan.