A compromise is that the two states pledged to work "as partners" on equal footing in building a global missile shield to cope with potential threat.
Local analysts say that Moscow could expect either to postpone the U.S. project until a Democratic administration sweeps into power in the coming months, or to downgrade its technology to relieve its threat to Russia.
Russia's President Vladimir Putin (R) and U.S. President George W. Bush shake hands after a news conference at the Bocharov Ruchey presidential summer residence at the Black Sea in Sochi April 6, 2008.
Bilateral ties
Putin said his face-to-face talks with Bush in Sochi, the last between the two leaders, was in "a quiet tone," although Russia-U.S. ties have plunged into a post-Cold War low in the last eight years.
"First of all, I would like to thank the American president for accepting the invitation to visit Sochi and sum up results of our eight-year joint work. I think George agrees that results of this work are generally positive," Putin said, opening Sunday's talks.
"We established a frank relationship at our first meeting in Ljubljana, and this relationship enabled the immediate discussion of pressing international and bilateral issues," he added.
"Our countries still have serious differences over certain problems and it is not easy to find points of contact," Putin told reporters, noting the two sides strived to shun negative impact and "the entire system of Russian-American relations is stable."