WASHINGTON – Poland is threatening to reduce the number of troops it has deployed in Iraq unless Poles are included in a waiver program allowing them to travel to America without first securing visas from the American embassy in Warsaw, American officials said.

The Polish prime minister, Marek Belka, first requested last month his country be included in the so-called tourist waiver program that benefits travelers from several European Union states. While visiting Washington he raised the issue in meetings with Secretary of State Powell and subsequently in a face-to-face with President Bush. Mr. Belka argued that being included in the program would indicate that Poland is considered a real partner by America.

Mr. Bush turned down Mr. Belka, said White House sources, but to the frustration of Washington that has not deterred the Polish prime minister from pressing the demand again and making it a key one in a list of requests that Warsaw is linking obliquely to whether or not it will reduce the Polish troop presence in central Iraq.

While the bargaining has prompted irritation in Washington, the Bush administration is keen to persuade Poland to maintain the number of troops it has in Iraq, fearful that any reduction would undermine its efforts to convince other countries to maintain forces there or to contribute forces for the first time, American officials said.

Poland has 2,400 troops in Iraq, making the Polish contingent the largest after America and Britain. But according to opinion surveys, the majority of Poles disapprove of their country’s military commitment in Iraq and opposed Poland’s backing of the American-led war to oust Saddam Hussein.

With an eye toward upcoming elections, several senior Polish government officials have said publicly that there will be a reduction next year in the Polish contingent in Iraq.

Recently, the country’s deputy defense minister, Janusz Zemke, said: “The number of Polish soldiers in Iraq in 2005 will be a number significantly smaller than present.” The chief of the Polish army general staff, General Czeslaw Piatas, has mentioned a likely figure of 1,500.

“It isn’t that Polish troops are essential in military terms,” a senior American official told The New York Sun. “But we don’t need a reduction in their numbers now in political terms.”

Bush administration sources say that Mr. Belka has been assured that Poland will benefit in the future from reconstruction contracts in Iraq and there are discussions, too, about improving the terms of American loans enabling the Polish Air Force to buy F-16 fighter jets, although there remain some “differences of opinion” over the loan conditions. But Mr. Belka says that he is firmly committed to the goal of bringing about the abolition of American visas for Poles and publicly in Poland he has given the impression that his objective is attainable.

Polish-American talks will continue later this month when the deputy secretary of state, Richard Armitage, visits Warsaw. His mission will be a delicate one, says a Bush administration source. “He has to say no to the visa waiver program without offending the Poles and we have to come up with something that helps the government sell its Iraq policy to voters, especially at a time when Iraqi militants are targeting the foreign contingents and are hoping to force another country to withdraw its forces like the Philippines did.”

The visa waiver program that Mr. Belka would like Poland to join allows nationals from certain countries, mostly European ones, to enter America as tourists or business visitors for three months without obtaining visas in advance. Currently, 29 countries participate in the program and they have been allowed to join because they have had low rates of refusal for visas in the past and their nationals tend not to overstay their permitted time in America.