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

The deal to install 10 U.S. interceptor missiles just 115 miles from Russia’s westernmost frontier also has strained relations between Moscow and the West, ties that already troubled by Russia’s invasion of its former Soviet neighbor, U.S. ally Georgia, earlier this month.

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

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

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 Gen. 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 NATO Secretary General Jaap de Hoop dismissed them Tuesday as “pathetic rhetoric.”

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

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.

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

Poland and the United States spent a year and a half negotiating, and talks recently had snagged on Poland’s demands that the U.S. 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.

The U.S. 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.