Obama also referred to Iran, saying the US will go ahead with a plan to build a missile defense shield, "as long as the threat from Iran persists."
The US leader, however, added, "If the Iranian threat is eliminated, we will have a stronger basis for security, and the driving force for missile construction in Europe will be removed."
At a press conference later, Czech Prime Minister Mirek Topolanek said Obama's speech made it clear the US has every intention to build the antimissile shield.
But analysts say the system's future is shaky as Washington looks to "reset" relations with Moscow, which opposes the system.
"The United States needs to get relations with Russia back on track; it needs Russia's help on a range of issues," explains Lawrence Korb, a former Reagan defense official and now a senior fellow at the Center for American Progress, a liberal think tank in Washington.
Why the US needs Russian help