Analysts say relations between the two superpowers, particularly concerning missile defense plans for Europe, should improve since Obama was returned to the White House, The Washington Post reported Wednesday.
"He [Obama] had a limited amount of space for maneuvering in relations with Moscow over the past year," Sergei Markov, Political Research Institute director, told Interfax Wednesday, noting Obama also was constrained by Republican criticism of his administration's policy toward Russia.
In March during a nuclear security summit in Seoul, Obama could be heard off-mike telling then-Russian President Dmitry Medvedev that there was little he could do about Russia's concerns over a missile defense system until after the election, when he would have more flexibility.
Russia has demanded written guarantees the system wasn't aimed at the country. United States has offered verbal assurances so far but hasn't gone further.
Medvedev, now Russia's prime minister, congratulated Obama Wednesday via Twitter.
President Vladimir Putin sent a congratulatory message to Obama and planned to call him with a personal greeting, the Post said.
"In general, the Kremlin took the news about Barack Obama's victory in the elections very positively," Putin spokesman Dmitry Peskov said.
Many Russian opposition leaders indicated they were disappointed that Republican Mitt Romney wasn't elected, the Post said. They had shifted toward Romney, who called Russia a "No. 1 geopolitical foe" and had hoped Romney would be tougher toward Putin.