US President George W Bush and top Democrats have vowed to try to find "common ground" on Iraq, but a deadlock over funding for US troops remains.
Mr Bush met Democratic leaders at the White House, a day after he vetoed a bill linking war funding to a timetable for withdrawal of US troops from Iraq.
A vote in the House of Representatives earlier failed to gain the two-thirds majority needed to override his veto.
Each side has urged compromise as talks begin on drafting new legislation.
Politicians are increasingly talking of setting "benchmarks" for Iraqi leaders to meet, in place of a set timetable for pulling out of Iraq.
Both Republicans and Democrats appear keen to have agreed the war funding by the end of May, but negotiations are likely to be difficult.
The Bush administration has warned that funding for US forces in Iraq and Afghanistan will run out soon, but analysts say the Pentagon has sufficient financial reserves to last until mid-July.
Leaders of the Democrat-controlled US Congress signed the controversial bill on Tuesday, agreeing to $100bn (£50bn) in further funding on condition US combat troops begin to withdraw this year.
Mr Bush has said he will veto any bill that sets an "artificial" timetable for withdrawal, insisting that time is needed for the new strategy of a surge of reinforcements in Baghdad to succeed.
Welcoming Democratic leaders to Wednesday's White House meeting, Mr Bush said he was confident that they could reach agreement.
"Yesterday was a day that highlighted differences," he said. "Today is the day where we can work together to find common ground."
House Democratic Speaker Nancy Pelosi also promised to try to break the impasse.
"Whatever our differences, we owe it to the American people to find our common ground," she said.
"Of course, we must stand our ground if we can't find it. But we must strive to find that common ground."
The White House talks began shortly after lawmakers in the House of Representatives held a vote on overriding the president's veto.
As expected, the 222-203 vote in favour fell far short of the two-thirds majority needed to overturn the measure.
Speaking in the debate ahead of the vote, Ms Pelosi accused Mr Bush of having "turned a tin ear to the wishes of the American people".
She went on: "The president wants a blank cheque. The Congress will not give it to him."
Speaking on Wednesday morning to a US building contractors' association, Mr Bush asked for patience on his Iraq strategy, saying: "We are heading in the right direction."
The top US general in Iraq, David Petraeus, has said reducing forces could lead to increased violence.
It is not yet known what the so-called benchmarks for the Iraqi government will be, but they could include monitoring of the Baghdad government's co-operation with the US and requiring an Iraqi-run programme to disarm militias.
Republican Senate Minority Leader Mitch McConnell told Fox television that setting benchmarks for the Iraqi government "is the place where compromise would well be achieved".
Democratic House Majority Leader Steny Hoyer said he hoped the House would vote on a new war funding bill within a fortnight.
"We are going to fund the troops, we are not going to leave our troops in harm's way without the resources that they need."
The Senate last week voted largely along party lines 51 to 46 in favour of the legislation, which said the pull-out must start by 1 October and sets a target of completion by 31 March 2008.