SEOUL — Unaware that a microphone was recording him, President Obama asked outgoing Russian President Dmitry Medvedev Monday for breathing room until after Mr. Obama’s re-election campaign to negotiate on missile defense.

“On all these issues, but particularly missile defense, this, this can be solved, but it’s important for him to give me space,” Mr. Obama told Mr. Medvedev at the end of their 90-minute meeting, apparently referring to incoming Russian President Vladimir Putin.

Mr. Medvedev replied, “Yeah, I understand. I understand your message about space. Space for you…”

“This is my last election,” Mr. Obama said. “After my election, I have more flexibility.”

The Russian leader responded, “I understand. I transmit this information to Vladimir.”

The exchange was picked up by microphone of a Russian reporter as journalists were allowed into the meeting room for remarks by the two leaders. It was first reported by ABC News, which said it verified the conversation. A Washington Times reporter heard a portion of the tape that begins with Mr. Obama saying, “This is my last election.”

The two leaders are in Seoul for a nuclear security summit involving the heads of more than 50 nations. Mr. Obama and Mr. Medvedev were huddling close together in their respective chairs when the conversation took place.

White House deputy national security adviser Ben Rhodes, who attended the meeting, at first said he didn’t hear the exchange and couldn’t comment on it. Within an hour, however, Mr. Rhodes issued a statement via email that said the U.S. “is committed to implementing our missile defense system, which we’ve repeatedly said is not aimed at Russia.”

“However, given the longstanding difference between the U.S. and Russia on this issue, it will take time and technical work before we can try to reach an agreement,” Mr. Rhodes said. “Since 2012 is an election year in both countries, with an election and leadership transition in Russia and an election in the United States, it is clearly not a year in which we are going to achieve a breakthrough. Therefore, President Obama and President Medvedev agreed that it was best to instruct our technical experts to do the work of better understanding our respective positions, providing space for continued discussions on missile defense cooperation going forward.”

The image of Mr. Obama putting off a difficult national security question due to re-election concerns is the opposite of what the White House intended for this trip. Mr. Obama’s first event upon landing in Korea on Sunday was to visit the Demilitarized Zone separating North and South Korea for a photo-op of him gazing across no-man’s land at a forward Army observation post.

Mr. Medvedev told reporters that he believes missile defense talks between the two countries “could be more active.”

“I believe we still have time; time hasn’t run out,” Mr. Medvedev said. “And now we need to discuss and cooperate on various aspects on European missile defense. Now, in my view, time has come for discussions between technical aspects and, of course, we remain at our own positions, both the United States and Russian Federation.”

When he knew he was speaking for the microphones, Mr. Obama said only, “We’ve got more work to do between our two countries. Dmitry identified some areas of continued friction — missile defense being an example. And what we’ve agreed to is to make sure that our teams, at a technical level, are in discussions about how some of these issues can be resolved.”

The U.S. and its NATO allies are pursuing a missile defense shield, while Russia objects that it would compromise its security. Mr. Rhodes said the U.S. has continuously told the Russians that the shield is not being developed as a defense against Russia, and that the two nations should move forward on a broad range of nuclear weapons issues rather than bog down over the shield issue.

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