Obama made the assertion earlier this year regarding negotiations with Russia over a proposed missile defense shield, RIA Novosti reported Friday.
Meeting with Russia's then-President Dmitry Medvedev earlier this year, Obama said, "After my election, I have more flexibility." The remark was picked up by a microphone and broadcast by news media around the world.
Obama is a "sincere man" who "sincerely wants to implement positive change," newly elected President Vladimir Putin told state-owned television network RT earlier this week.
"But can he do it, will they let him do it?," Putin asked.
Obama's Republican opponent, Mitt Romney, has called Russia America's number one enemy.
Both Obama and Putin are trying to "reset" the state of relations that existed before President George W. Bush, said Alexei Pushkov, head of the international affairs committee in Russia's lower house of parliament.
Pushkov predicted "relations will be more complicated and not nearly as warm as they were portrayed three years ago" when the "reset" policy was announced.
The "reset" policy is viewed by Russian officials as a course correction that's already done, commented Angela Stent, director of the Center for Eurasian, Russian and East European Studies at Georgetown University.
"The question from the Russian side is: Where do we go from here?" Stent said.
Moscow sees the United States needing cooperation from Russia on issues such as Afghanistan more than Russia needs the United States, she added.
What Russia wants more is investment by major U.S. businesses, said Dmitri Trenin, director of the Carnegie Moscow Center. If that were to happen, relations between the two countries would be smoothed considerably, he said.