Kerry said he hoped the talks would be constructive and allow the nations to find a way to "rebuild and strengthen the relationship between the United States and Russia by proving that we know how to solve some serious problems together and building from there."
Kerry hailed a cease-fire in Syria brokered by the U.S. and Russia, saying it had allowed Syrians "to taste and smell the possibilities of what it means to have a huge reduction in violence and to receive humanitarian assistance."
In a playful start to the talks, Putin noted that Kerry walked off the plane carrying his briefcase himself and joked that he must have brought some cash to bargain with Russia.
Kerry replied, "When we have a private moment I will show you what's in my briefcase and I think you will be surprised." Switching to a serious tone, the Russian leader said he hoped for a constructive discussion that would "allow us to make our positions on Syria and Ukraine closer."
More From This Section
The main Syrian opposition group has wrapped up the latest round of indirect peace talks by urging Russia to "use its leverage" on Assad's government to fulfil international hopes for a political transition.
In Geneva, Bassma Kodmani, a leader of the opposition High Negotiations Committee, told reporters today that it wants greater access for humanitarian aid and decried continued sieges by government forces on Syrian municipalities.
Kerry's meetings were arranged after Putin made a surprise announcement last week that Russian troops would partially withdraw from Syria after five months of military operations in support of Assad's government.