SEOUL—President Barack Obama was overheard confiding to Russia’s president that he would have to await his re-election before addressing the divisive issue of global missile defense, an unscripted moment that touched off a political backlash at home.

Mr. Obama told Russian President Dmitry Medvedev that he can’t resolve the issue before the November election, but that afterward, he would have more “flexibility.” The comments were picked up by a live microphone.

Republicans seized on the exchange to suggest that Mr. Obama may talk tough during the campaign but then cave to Moscow once re-elected. They also questioned what else Mr. Obama has in store for a second term that he doesn’t want to disclose now.

Sen. John McCain (R., Ariz.) said the words were those of “a real Etch A Sketch leader,” comparing them to a political adviser’s ill-fated comment last week that the campaign of GOP front-runner Mitt Romney would alter its positions for the general election, “like an Etch A Sketch.”