MOSCOW—Russian President Vladimir Putin said the re-election of President Barack Obama could improve relations with the U.S., but that he was also prepared to work with Mitt Romney, calling the Republican candidate's tough stance on Russia "pre-election rhetoric."

In contrast to what had been viewed as a chilly attitude toward Mr. Obama, Mr. Putin called his U.S. counterpart "a genuine person" who "really wants to change much for the better." Speaking to Russia's state-run RT television channel, he said a second Obama term could help solve disputes over missile defense.

The comments will likely be seized on by the Romney campaign, which in recent months has sharply criticized Mr. Obama's so-called reset of relations with the Kremlin and pushed a harder line.

Relations with Russia first heated up the campaign in March, when Mr. Obama was inadvertently caught on an open microphone telling Mr. Putin's predecessor, Dmitry Medvedev, that he would have "more flexibility" after the election to address Russia's concerns over the proposed U.S. antimissile shield in Europe.

The U.S. says the defense system is designed to protect against a possible missile attack from Iran, but Moscow says the interceptors could neuter Russia's nuclear arsenal.