President Bush and Congressional leaders began negotiating a second war funding bill yesterday, with Democrats offering the first major concession: an agreement to drop their demand for a timeline to bring troops home from Iraq.

Democrats backed off after the House failed, on a vote of 222 to 203, to override the president’s veto of a $124 billion measure that would have required U.S. forces to begin withdrawing as early as July. But party leaders made it clear that the next bill will have to include language that influences war policy. Senate Majority Leader Harry M. Reid (Nev.) outlined a second measure that would step up Iraqi accountability, “transition” the U.S. military role and show “a reasonable way to end this war.”