MOSCOW -- Vladimir Putin, Russia's current premier and former president, gave the clearest signal to date that he is considering a return to his old job, saying that he and his handpicked successor President Dmitry Medvedev, will decide who runs in 2012.

In a 2½-hour question-and-answer session with some 45 Russia experts from around the world, Mr. Putin also gave his most detailed assessment of relations with the U.S. since President Barack Obama visited Moscow in July. Mr. Putin said he was "mildly optimistic" over...