"If the by-product of it is that the Russians feel a little less paranoid and are now willing to work more effectively with us to deal with threats like ballistic missiles from Iran or nuclear development in Iran, you know, then that's a bonus."
Obama on Thursday announced that the US was scrapping plans to place the missile defence shield in Poland and the Czech Republic.
The Bush administration had pushed hard for the shield, arguing that Iran was developing long-range missiles alongside its controversial nuclear programme.
Obama said that instead of a shield, there will be a different missile-defence plan relying on a network of sensors and interceptor missiles based at sea, on land and in the air.
His announcement raised questions of whether the decision was done in part to appease Russia and win its help in other areas, mainly in confronting the potential of a nuclear-armed Iran.
Vladimir Putin, Russia's prime minister, on Friday praised Obama's decision as "brave."
"Russia had always been paranoid about this, but [former president] George Bush was right, this wasn't a threat to them," Obama said.