Republicans in the US House of Representatives have met President Barack Obama amid renewed efforts to avert a looming debt crisis.
Both sides described the 90-minute meeting as useful but said no decision was made. They agreed to keep talking.
Republicans have offered the president a short-term debt limit increase to stave off default.
In return they want Mr Obama to further negotiate on the budget dispute that has partially closed the US government.
“It was a very adult conversation,” said Republican Hal Rogers who attended the meeting. “Both sides said they were there in good faith.”
The White House said in a statement: “The president looks forward to making continued progress with members on both sides of the aisle.”
Officials have warned the US risks default on 17 October 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.
It is not clear if Republicans are willing to drop entirely their attempts to defund or delay Mr Obama’s 2010 healthcare law – demands which brought about the government shutdown, the first in 17 years.
Leading Republican Pete Sessions said the two sides were working on “defining parameters to see if we can make progress”.
Earlier, House of Representatives Speaker John Boehner told reporters: “What we want to do is to offer the president today the ability to move a temporary increase in the debt ceiling in agreement to go to conference on the budget for his willingness to sit down and discuss with us a way forward to reopen the government.”
“It’s time for leadership,” the Ohio Republican said. “It’s time for these negotiations and this conversation to begin.”
A spokesman for Mr Boehner told reporters the deal offered was a “clean” increase of the debt limit, with no additional policies attached.
It would only last six weeks – until 22 November.
Reacting to the offer, White House press secretary Jay Carney told a daily press briefing the president was glad that “cooler heads” seemed to be prevailing in the House.
The likelihood is that markets around the world would plunge and global interest rates would rise”
But he added: “He will not pay ransom in exchange for the Republicans in the House doing their job.”
Earlier on Thursday, Democratic Senate leader Harry Reid said the Senate would “look at anything” the House sent to them, but they would not engage in negotiations with Republicans prior to reopening the government.
The impasse over the debt limit has already rattled markets and increased the interest rate for one-month US Treasury bills. But US stock markets rebounded on Thursday on news of a possible breakthrough.
Democratic Senate finance committee chairman Max Baucus said the Republican campaign to undermine the healthcare law in return for agreeing to end the shutdown was “not up for debate” and would not happen.
First intelligence from up on the Hill suggests that getting enough Republican votes could be hard”
Hundreds of thousands of federal employees have been out of work since the shutdown began, and private firms, from arms makers to motels, have begun to lay off workers.
About 15,000 private-sector employees have filed for unemployment benefits due to the shutdown, the US labour department said on Thursday.
And governors in at least four western states – Utah, South Dakota, Arizona and Colorado – have asked for authority to reopen national parks within their borders because of the economic impact of the closures.
On Thursday, Mr Obama signed legislation restoring death benefits to families of US troops who have died since the government closed. The shutdown prevented processing of the payments, typically made within days of the soldier’s death.
The president also met House Democrats at the White House on Wednesday and told them he would prefer a longer-term increase to the nation’s $16.69 trillion (£10.47 trillion) debt ceiling.
But the president said he was willing to accept a short-term rise in the borrowing cap to “give Boehner some time to deal with the Tea Party wing of his party”, Representative Peter Welch told the Associated Press news agency after the meeting, referring to a Republican faction of hard-core conservatives.
The stalemate has harmed the approval ratings of both Democrats and Republicans, but the Republicans’ popularity has taken the worst hit and is now at a record low of 28%, according to a Gallup poll.
Earlier, Treasury Secretary Jack Lew told a congressional panel that skipping a payment on US debt would trigger a potentially profound financial crisis.
“It would be chaos,” Mr Lew told the Senate hearing.
Since the US hit its debt ceiling in May, the treasury has been using what are called extraordinary measures to keep paying the bills, but those methods will be exhausted by 17 October, Mr Lew has said.