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Eight other countries have withdrawn all of their troops from the coalition since February: the Dominican Republic, Honduras, Nicaragua, Norway, the Philippines, Singapore, Spain and Thailand.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

Poles' unhappiness has been increased by their perception that the Bush administration has been stingy in providing reconstruction work to Poland and has unfairly refused to ease the stiff post-Sept. 11 visa requirements placed on its citizens and those from neighboring countries. The rules require visitors from Eastern Europe — unlike those in Western Europe — to pay a $100 application fee and be personally interviewed before receiving a visa.

Polish officials have entreated the White House to ease the rules, but so far without result. One Polish newspaper recently said Poland is like a woman who is taken out on a date one night, then ignored when her date meets her on the street the next morning.

On Oct. 4, Polish Defense Minister Jerzy Szmajdzinski became the first Polish official to raise the possibility of withdrawal. He said officials wanted to wind down the mission by the end of 2005.

Cook said that although the Poles, Ukrainians and Moldovans did not want to pull out abruptly, as the Spanish did earlier in the year, they had been signaling that they wished to leave before too long.

The departure creates a domestic political problem for Bush, who has been emphasizing the solid support of the "coalition of the willing," Cook said. And it creates a foreign policy difficulty, he added, because it would make it more difficult for the Bush administration to recruit other countries to help out in Iraq.

At the same time, Cook said, it might foretell difficulties for Democratic presidential nominee John F. Kerry, who has promised that if elected he would be able to bring in more help from allies.

Mark Brzezinski, a specialist on Eastern Europe and former staff member at the National Security Council, noted that Polish officials have been making seemingly conflicting statements on the future of the deployment.

"The fact they're going back and forth does not indicate a stalwart endorsement of Bush's policy," said Brzezinski, who has been an informal adviser to the Kerry campaign. He emphasized that he was speaking only for himself.