The continued lobbying comes after senators from the Democratic Party and from Bush's Republican Party announced agreement on a non-binding resolution opposing Bush's plan to increase U.S. troop deployment in Iraq by 21,500 troops.
The resolution says it is "not in the national interest of the United States to deepen its military involvement in Iraq."
The resolution would not have the force of law if passed by the Senate, but correspondents say it could set up a clash between the presidency and Congress over the course of the war.
Senator Chuck Hagel (Republican, Nebraska), who helped draft the resolution, said he would do everything he could to stop Bush's war policy.
"I think it is dangerously irresponsible to continue to put American lives in the middle of a clearly defined, tribal-sectarian civil war," Hagel said. "It's wrong."
The measure was drafted by Hagel and Democratic senators Joseph Biden (Delaware) and Carl Levin (Michigan). It is not clear when the Senate might vote on the measure.
(complied from agency reports)
The Imam Al-Mahdi Army on parade (epa)
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THE COMPLETE PICTURE: Click on the image to view RFE/RL's complete coverage of events in Iraq and that country's ongoing transition.