The US House of Representatives last night approved a Bill that will fund the war in Iraq for almost three months but will require Mr Bush to report to Congress in July before further funds are released.
The 221-205 vote was largely along party lines and sent the measure to the Senate, where Majority Leader Harry Reid, a Democrat, is seeking a compromise with the White House and Republicans.
Under growing political pressure from Republicans, President Bush coupled his veto threat with a sign of flexibility. Visiting the Pentagon, he said he was willing to sign a military money Bill that includes political and military goals for the Iraqi government.
Mr Bush's decision to negotiate with Congress on a new Bill came two days after a group of moderate Republicans warned him that he could not depend on their support over Iraq for much longer.
Washington is impatient with Iraqi progress in introducing legislation to promote reconciliation between Shias and Sunnis, including a law that would share the country's oil revenues.
Speaking at the Pentagon after a briefing on Iraq from military commanders, Mr Bush said: "As we have surged our forces, al-Qaeda is responding with their own surge. Al-Qaeda is ratcheting up its campaign of high-profile attacks, including deadly suicide bombings carried out by foreign terrorists.
"These attacks are part of a calculated campaign to reignite sectarian violence in Baghdad, and to convince the people here in America that the effort can't succeed," he said.