WASHINGTON — The Senate Foreign Relations Committee approved a nonbinding resolution against President Bush’s plan to send more troops to Baghdad as lawmakers begin to act on their growing discontent with the war in Iraq.

The panel voted 12–9, with one Republican, Senator Hagel of Nebraska, joining all the Democrats to approve the measure that declared “increasing ” American forces in Iraq is “not in the national interest.”

The committee chairman, Senator Biden, a Democrat of Delaware, said the committee’s action should prod Mr. Bush to change his strategy. “How can that not have an impact?” he told reporters after the vote.

The resolution, written by Messrs. Biden and Hagel and Senator Levin, a Democrat of Michigan, now goes to the full Senate as early as next week, where it will probably face amendments from both Democrats and Republicans, as well as a competing resolution from Senator Warner, a Republican of Virginia, who “disagrees” with the president’s plan to “augment” American forces in Iraq.

Mr. Biden said he would talk with Mr. Warner to try to agree on final language that would receive the most support among senators of both parties. “My hope is we can broaden this bipartisan coalition,” he said.

In an effort to entice more committee Republicans to back the resolution, Mr. Biden, shortly before the final vote, replaced the word “escalating,” which some Republicans called partisan, with “increasing.”

Mr. Biden said he wasn’t disappointed that more Republicans didn’t back the measure because all of them “dismissed” the president’s plan during committee debate.

“I am not confident that President Bush’s plan will succeed,” Senator Lugar, a Republican of Indiana, said, though he voted against the measure. “With the passage of this resolution, I believe we would be letting our frustration get the better of us.”

Mr. Biden, who is a candidate for the 2008 Democratic presidential nomination, said Mr. Bush’s plan to send 21,500 more American forces to Baghdad would represent a “significant mistake” in American policy.

Last night, in his State of the Union address before both houses of Congress, Mr. Bush asked lawmakers to give his plan time to work.

“I chose this course of action because it provides the best chance of success,” Mr. Bush told lawmakers. “I ask you to give it a chance.”

Senators on both sides of the debate acknowledged the resolution would have no legislative power to influence the president’s action. Senator Reid of Nevada, the majority leader, has said passage by an overwhelming vote may finally force Mr. Bush to bend to public opinion and change strategy.

However, lawmakers are also considering further steps against the president’s plan that would be binding, including placing conditions on the next war-funding request Mr. Bush is likely to send to Congress for approval next month.

Mr. Biden said yesterday’s resolution is the most immediate step lawmakers can take and that there are others if the strategy doesn’t change.

“Unless the president demonstrates very quickly that he is unlikely to continue down the road he’s on, this will be only the first step,” Mr. Biden said.