WASHINGTON — The prime minister of Poland told his Parliament on Friday that he would begin drawing down Polish troops in Iraq in January, another blow to a U.S.-led coalition that has lost nearly one-third of its members this year.

Addressing his Parliament before a vote of confidence, Prime Minister Marek Belka promised, "We will not remain in Iraq an hour longer than is sensible (and necessary to return stability to Iraq)."

Polish officials had been hinting at a troop reduction for nearly two weeks. The 2,500 Polish troops have a special importance to the international coalition because Warsaw's forces have led an 8,000-member international division in south-central Iraq and have been praised repeatedly by President Bush for their service.

Eight other countries have withdrawn all of their troops from the coalition since February: the Dominican Republic, Honduras, Nicaragua, Norway, the Philippines, Singapore, Spain and Thailand.

Officials of two other countries, Ukraine and Moldova, have indicated a desire to withdraw, and the subject has been under discussion in several other countries, such as the Netherlands and Denmark.

Many members of the coalition have relatively few troops to withdraw. Of the 30 allied forces, only six have 1,000 or more troops in Iraq.

Belka didn't provide a schedule for the drawdown, but other Polish officials have suggested that they might reduce the force by 40 percent in the first cut and pull out the last troops by the end of next year.

Adam J. Ereli, a U.S. State Department spokesman, said that although the Poles might reduce their troop contingent, they have promised U.S. officials that they would not withdraw fully until the mission is completed.

"We have no concern that the Poles are pulling out; to the contrary, they're telling us they're not pulling out," Ereli said. "Whether they change the number of troops, or their profile, that's up to them . . . we don't see in this announcement any lessening of the commitment."

The strength of the coalition has been a major issue in the U.S. presidential debates. President Bush repeatedly cited the Poles as a steadfast ally.

Poland's announcement "is not a great signal, and that's an understatement," said Steven A. Cook, a Middle East specialist at the Council on Foreign Relations in New York.

Poland has been one of the most pro-American countries in Europe, and the Polish military contributed special forces to the invasion of Iraq in March 2003. But Polish public opinion gradually has turned against the deployment, and opinion polls show that more than three-quarters of Poles believe their forces should come home.