Under the bill, further funding would be dependent on events in Iraq meeting certain, as yet undefined, benchmarks of progress.

President George W Bush said he would veto the bill but hinted a compromise was possible, saying the idea of setting benchmarks "made sense". Mr Bush has already vetoed one bill linking funding to troop withdrawal.

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.

The new bill would ring-fence about half of the money, US$52.8 billion that Mr Bush has requested to fund the war in Iraq.

Lawmakers would then vote in July on whether to release this money on the basis of a report from Mr Bush on progress towards political, economic and security targets.

Earlier on Thursday, the House of Representatives rejected a separate and largely symbolic bill calling for US troops to withdraw from Iraq within 180 days of the legislation being passed.

The vote, proposed by a group of anti-war Democrats, was rejected by 255 votes to 171.