"Although there have been some differences of the last several months, we both agree that we should be supportive of [U.N-African League special envoy] Kofi Annan's efforts to try to end some of the bloodshed that's taking place within Syria and move towards a mechanism that would allow for the Syrian people ultimately to have a representative and legitimate government that serves their interest," Obama said in a media event before the Nuclear Security Summit began in Seoul.
Medvedev agreed, saying the two world leaders discussed a number of international issues, "including the most difficult ones, such as Syria."
Medvedev said he had a "very good meeting" with Annan.
"We believe that his mission is very good and we hope that he will be able to reach good results, and to somewhat appease, at least initially, the situation, and would help to establish communication between various public groups and forces that exist in Syria. And yesterday [Sunday], I expressed my every support to Mr. Annan."
Russia wants to ensure that there aren't "greater problems than we already have, and that the threat of the civil war is averted," Medvedev said.
Russia, along with China, has blocked U.N. efforts to criticize or sanction Syrian President Bashar Assad for the violent response to anti-government protests that began more than a year ago. Russia and China are trade partners with Syria.
Obama told Medvedev he believed part of the transition envisioned in Annan's initiative would involve Assad leaving power so a government could be installed "that's responsive to the Syrian people," Deputy National Security Adviser for Strategic Communications Ben Rhodes said.
"But the two leaders had expressed an interest in working together going forward in a way that strengthens Kofi Annan and stops the violence in Syria and enables a transition to take place that is, again, far preferable to the type of conflict that we've seen and the potential for even further civil war," Rhodes said.
Medvedev and Obama also discussed the U.S.-led missile defense shield in Europe, which Russia maintains would threaten its security. The United States said it would be meant as a defense against attacks from countries such as Iran.
"I believe we still have time to agree on a balanced solution, and I believe that the good experience Barack and myself have gained while working on the START Treaty [on nuclear arms reductions] will help us and be very useful when finding [a] solution to this very difficult problem," Medvedev said.
Obama said the two agreed to make sure the negotiating teams "at a technical level are in discussions about how some of these issues can be resolved."
The two also discussed nuclear issues in Iran and North Korea.
"We agreed that, as two of the world's leading powers, it's absolutely critical that we communicate effectively and coordinate effectively in responding to a wide range of situations that threaten world peace and security," Obama said.
The two countries "probably enjoyed the best level of relations … during [last] three years than ever during the previous decades," Medvedev said.
He noted the signing of a treaty on nuclear arms reductions and U.S. support of Russia's ascension to the World Trade Organization.
"Let me just say that at a time of great challenges around the world, cooperation between the United States and Russia is absolutely critical to world peace and stability," Obama said.
Medvedev leaves office in the spring when Prime Minister Vladimir Putin begins his third term as president.
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