Kerry said the two countries both believe the meeting should take sooner rather than later, but acknowledged it might not be possible until August or later. Such an international meeting, which has been delayed several times before, is known as "Geneva II" because it follows a Syria meeting in the Swiss city in June 2012.
Kerry spoke outside the US Embassy in Brunei after a 90-minute-plus meeting with Russian Foreign Minister Sergey Lavrov on the sidelines of an Asian security summit.
"Our objective remains the same that to recognize the notion that there really isn't a military victory, per se, for Syria that keeps Syria as a country," Kerry said. "And No. 2, that we have an obligation to try to work towards a peaceful resolution because a peaceful settlement is the best way to save the state of Syria and to minimize destruction."
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Last month, Lavrov said the US was sending conflicting signals to the rebels. While the US said it favored a peace conference in Geneva, Lavrov said, talk about a possible no-fly zone encouraged the opposition to step up fighting instead of sitting down for talks.
"The message the opposition is getting: Guys, don't go to Geneva, don't say you are going to negotiate with the regime, soon things will change in your favor," Lavrov said then.
Syria was also the focus of Kerry's discussion with Turkish Foreign Minister Ahmet Davutoglu. A senior State Department official said the two discussed ways to strengthen support to the opposition and step up plans for an international conference to resolve the crisis.
The official, who spoke on condition of anonymity to disclose details of the closed-door meeting, said Kerry and his Turkish counterpart also discussed how to expand the Syrian people's access to humanitarian aid.
He said both men expressed concern over recent Assad regime attacks on civilians in the central province of Homs and the influx of fighters from the Lebanese militia Hezbollah.
The Russian state news agency ITAR-Tass reported that the two did not discuss Snowden, but Kerry said he raised US concerns and hoped Lavrov would pass them to Russian officials.