WASHINGTON — President Bush promised Poland’s visiting prime minister yesterday that America would help modernize the country’s military, as Poland moved closer to joining a American-sponsored missile-defense system.

Mr. Bush’s Oval Office meeting with Prime Minister Donald Tusk followed a similar conference in February with the Czech prime minister, who said Prague was close to an agreement with Washington on the missile-defense arrangement.

America says it is seeking to install a missile-detection radar system in the Czech Republic and interceptor missiles in Poland to defend against missiles launched in the Middle East.

With Mr. Tusk at his side, Mr. Bush said that, “before my watch is over,” America and Poland would “come up with a modernization plan” for Polish forces, which are seeking to acquire a Patriot anti-missile system. Mr. Bush’s aides insisted that Poland’s diminished objections to the American deployment of missile interceptors on Polish territory was not a quid pro quo for military aid. However, the president linked the two, pledging the modernization assistance, and then saying, “along those lines,” that he and Tusk discussed the risk posed by “a missile with dangerous materials in its warhead.”

The proposed missile-defense network has become perhaps the most sensitive issue in American-Russian relations. President Putin has denounced it as a threat to his nation’s defense. Mr. Bush has insisted that it would be used to protect part of Europe and America from any missiles launched by Iran or terror groups.

Mr. Bush said a missile equipped with nuclear, chemical, or biological warheads was “the most significant” security threat of the 21st century, and he assured Mr. Tusk that “this system is not aimed at Russia.”

He said he would continue to give Mr. Putin similar assurances. Mr. Tusk, speaking through a translator, called the missile-defense system and the modernization of Polish forces “very good.” He expressed support for the proposal to protect Poland from “any undue security risks” but cautioned that work remained on the diplomatic front, saying, “a strategy on paper is a little different from the details.”

The press secretary for the White House, Dana Perino, said that the Pentagon would evaluate Poland’s air defense needs and that Secretary of State Rice and Defense Secretary Gates would review those needs with Polish officials.

The system the administration wants to build would use the radar to spot missile launches and send interceptors to ram the missiles above the Earth’s atmosphere. Iran has developed medium-range missiles capable of striking Israel and parts of Europe.

The Bush administration predicts that Iran will be able to develop long-range ballistic missiles by 2015. The missile-defense system could be completed by 2012 or 2013, officials have said.

Even before formal negotiations over basing interceptor missiles on Polish soil began in 2007, Polish officials demanded America provide Patriot anti-missile batteries to the Polish armed forces. They argued that a new American missile-defense site would make Poland a target of Russian rockets.