WARSAW, Poland — Secretary of State Condoleezza Rice and her Polish counterpart signed a deal today to build an American missile defense base in Poland, an agreement that prompted an infuriated Russia to warn of a possible attack against the former Soviet satellite.

Ms. Rice dismissed blustery comments from Russian leaders who say Warsaw’s hosting of 10 American interceptor missiles just 115 miles from Russia’s westernmost frontier opens the country up to attack.

Such comments “border on the bizarre frankly,” Ms. Rice said, speaking to reporters traveling with her in Warsaw.

“When you threaten Poland, you perhaps forget that it is not 1988,” Ms. Rice said. “It’s 2008 and the United States has a … firm treaty guarantee to defend Poland’s territory as if it was the territory of the United States. So it’s probably not wise to throw these threats around.”

The deal, which Washington sought as a way of defending the America and Europe from a hypothetical threat of long-distance missiles from Iran, has strained relations between Moscow and the West. Those ties were already troubled by Russia’s invasion of its former Soviet neighbor, American ally Georgia, earlier this month.

Speaking to reporters traveling with her, Ms. Rice said, “the Russians are losing their credibility.”

Ms. Rice and Polish Foreign Minister Radek Sikorski signed the deal this morning.

“It is an agreement which will help us to respond to the threats of the 21st century,” she said afterward.

The Polish Prime Minister, Donald Tusk, said the agreement came after tough but friendly negotiations.

“We have achieved our main goals, which means that our country and the United States will be more secure,” he said.

After Warsaw and Washington announced the agreement on the deal last week, top Russian General Anatoly Nogovitsyn warned that Poland is risking attack, and possibly a nuclear one, by deploying the American missile defense system, Russia’s Interfax news agency reported.

Poles have been shaken by the threats, but the NATO Secretary General, Jaap de Hoop, dismissed them yesterday as “pathetic rhetoric.”

“It is unhelpful and it leads nowhere,” he told reporters at a NATO meeting in Brussels, Belgium.

Today, Russia’s Foreign Ministry issued a statement saying the American missile shield plans are clearly aimed at weakening Russia and that Moscow’s response to their further development will go beyond diplomacy.

Many Poles consider the agreement a form of protection at a time when Russia’s invasion of Georgia has generated alarm throughout Eastern Europe. Poland is a member of the European Union and NATO, and the deal is expected to deepen its military partnership with Washington.

The Polish President, Lech Kaczynski, also expressed “great satisfaction” at the outcome of the long months of negotiations.

Poland and America spent a year and a half negotiating, and talks recently had snagged on Poland’s demands that America bolster Polish security with Patriot missiles in exchange for hosting the missile defense base.

Washington agreed to do so last week, as Poland invoked the Georgia conflict to strengthen its case.

The Patriots are meant to protect Poland from short-range missiles from neighbors — such as Russia.

America already has reached an agreement with the government in Prague to place the second component of the missile defense shield — a radar tracking system — in the Czech Republic, Poland’s southwestern neighbor and another formerly communist country.

Approval is still needed the Czech and Polish parliaments.

No date has been set for the Polish parliament to consider the agreement, but it should face no difficulties in Warsaw, where it enjoys the support of the largest opposition party as well as the government.