City Council members yesterday introduced two resolutions calling for the withdrawal of American troops from Iraq, propelling the council into a policy debate in which its members acknowledge they have little power but many strong opinions.

The resolutions both signaled an opposition to the war but differed in their wording. One, co-sponsored by the speaker, Gifford Miller, called for a “change of policy in Iraq” and the “strategic withdrawal” of American forces. Six council members sponsored a separate resolution demanding that the government “immediately commence an orderly and rapid withdrawal” of troops. The second statement also instructed that it be sent to President Bush and members of the state congressional delegation.

“We’ve lost too many New Yorkers and too many Americans,” Mr. Miller said. “We need, as a country, to develop a strategy for withdrawal.”

A council member from Queens, James Sanders Jr., told colleagues at yesterday’s stated meeting that America “finds itself more endangered” after invading Iraq.

“We are in a foolhardy crusade,” Mr. Sanders said. “We must rethink our position.”

One or both of the resolutions are expected to pass the Democrat-dominated body, but some lawmakers blasted the nonbinding decrees, saying it is a waste of the council’s time to weigh in on foreign policy matters that are beyond its jurisdiction.

“What’s the point?” Simcha Felder, a Democrat of Brooklyn asked. “I don’t believe the New York City Council should be involved in introducing resolutions that are international in nature.”

Mr. Felder said he supported the war and President Bush, but that even if he opposed it, he would not sign on to a resolution of protest. “What’s the City Council going to do about it?”

The council’s Republican leader, James Oddo, said the resolutions would prompt unnecessary bickering in a body usually known for having few close votes. “Why are we going down this divisive road?” he asked. “It will have a majority of members, but not the usual majority in this body.”

A co-sponsor of the statement calling for immediate withdrawal, Charles Barron, disputed the suggestion that it was inappropriate for the council to opine on international issues.

“That’s garbage,” Mr. Barron said. “This is an international city. The political expressions of this body have influence on state and federal legislation.

“We don’t have power, but we have influence,” he said. “There are a lot of non-binding resolutions that we pass. It’s the influence.”

Mr. Miller, who recently lost the Democratic mayoral nomination in a primary in which he drew 10% of the vote, said it was the council’s responsibility to draft resolutions on issues of national importance, and that he saw no reason to stay silent on the war. “For better or for worse, people actually do care what the City Council has to say on this subject,” he said. “Speaking out on behalf of New Yorkers is part of our job.”

The current resolutions are not the first time the council has sought to express its opinion on the Iraq war. During the lead-up to the invasion in early 2003, council members heatedly debated the question of whether to draft an anti-war resolution, versions of which more than 100 other American city councils had passed. Some adamantly supported a strong statement of opposition, while others at the time were hesitant to do so just a year and a half after the terrorist attacks of September 11, 2001.

Ultimately, the chamber passed a softer statement that cited “great concern” about the direction of American policy but supported military action as a last resort in Iraq. The stance appeased some, but not all council members.

“I was embarrassed by the war resolution,” Mr. Oddo said. “The one positive thing I can say about the council on this issue is that it’s consistent. It’s consistently bad.”