The US House of Representatives has passed a bill which would fund military operations in Iraq to the end of July.
President Bush says he will veto the new bill in its current form
Further funding would be dependent on events in Iraq meeting certain, as yet undefined, benchmarks of progress.
President Bush has already vetoed one Iraq funding bill and said he opposed the new proposal, but did say that the idea of benchmarks "made sense".
The move came as the White House and Democrats struck an accord on standards for bilateral free trade deals.
The deal was announced by House Speaker Nancy Pelosi, a Democrat, who hailed it as a result of the Democratic triumph in last year's congressional elections.
Under the new agreement countries seeking direct trade agreements with the US will have to abide by minimum standards on labour and environmental issues.
Historically, Democrats have been lukewarm on supporting free trade deals without built-in minimum standards.
Correspondents say the White House agreed to the proposal in an effort to secure Democratic support in Congress for free trade deals, including pending deals with Peru, Ecuador, Panama and Colombia.
On Iraq, the House passed its latest funding bill late on Thursday by 221 votes to 205.
The bill would immediately release some $43bn (£21.8bn) of funding requested by Mr Bush for the war in Iraq.
However it would also ringfence almost $53bn for release only after a demonstration in July that progress had been made towards political, economic and security targets.
Although the new bill has passed in the House, most Republicans oppose it.
That makes it unlikely it will be passed in the Senate, where the Democrats have a very slender majority.
Mr Bush himself has resisted attempts to link war funding to withdrawal, and said such "piecemeal" funding would not work.
However, he is coming under increasing pressure from some Republicans, as well as Democrats, over progress in Iraq.
Earlier this week a group of 11 Republican congressmen met Mr Bush at the White House to warn him that he cannot rely on unqualified support for his policy past September.
After Thursday's vote Ms Pelosi repeated the Democratic assertion that there will be no "blank cheque" for President Bush to fight the Iraq war.
"This is a bill he should like," she said.
"It has his benchmarks, it asks for a progress report, he must have some confidence in what he is doing, and then leave it up to the Congress to make a judgment in July, what could be fairer than that?"
But Mr Bush maintained his opposition to the bill, insisting he would again wield his veto to strike it down.
"I'll veto the bill if it is this haphazard, piecemeal funding and I made that clear," he said. "We reject that idea. It won't work."
But he did signal that he could be in favour of setting benchmarks, saying that people "on both sides" had told him they could work if common ground was found.
Mr Bush also said the Iraqi government - which plans to take a two-month summer recess - needed to "speed up their clock" on measures designed to bring stability to the country.