The leaders of the Czech Republic and Poland say they are in favour of letting the US build parts of its missile defence system on their soil.
Russia feels threatened by the US missile defence plan
Czech Prime Minister Mirek Topolanek said he agreed with his Polish counterpart that they would probably respond positively to a US request.
The US wants to build a missile interceptor site in Poland and a radar station in the Czech Republic.
Russia has condemned the plan, saying it will be able to target the sites.
"If the governments of Poland and the Czech Republic take a decision to this effect, the strategic missile troops will be capable of having these facilities as targets," said Gen Nikolai Solovtsov, commander of Russia's missile forces.
The US says the missile defence in Central Europe is designed to guard against possible missile attacks from the Middle East or North Korea.
Both Mr Topolanek and Polish Prime Minister Jaroslaw Kaczynski stressed that the missiles would not be directed against Russia. They were speaking after talks in Warsaw on Monday.
Mr Topolanek could still struggle to get the plan approved by both houses of the Czech parliament, correspondents say.
His three-party, centre-right governing coalition recently won a vote of confidence, but controls just 100 of 200 seats in the lower house.
There is opposition to the scheme in the Czech Republic, protesters having recently rallied against it in Prague.
There is also public opposition in Poland to the plan.
The US has already built missile interceptor sites in Alaska and in California, but says it needs to expand into Europe to counter growing threats from further afield.