Mr 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”.
Mr Kerry hailed a US- and Russian-brokered ceasefire in Syria, adding that it had allowed the Syrians “to taste and smell the possibilities of what it means to have a huge reduction in violence and to receive humanitarian assistance”.
“We obviously also have some ideas about this and how we can most effectively make progress in Geneva and begin the very serious and difficult work of the transition,” he said.
In a playful start to the talks, Mr Putin noted Mr Kerry walked off the plane carrying his briefcase and joked he must have brought some cash to bargain with Russia. Mr 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”.
Mr Kerry is seeking clarity from Mr Putin and foreign minister Sergey Lavrov as to where Russia stands on a political transition for Syria, particularly on the future of Syrian president Bashar Assad, now that a fragile truce is holding and UN-brokered peace talks are under way.
The main Syrian opposition group has wrapped up the latest round of indirect peace talks by urging Russia to “use its leverage” onMr Assad’s government to fulfil hopes for a political transition.
In Geneva, Bassma Kodmani, a leader of the opposition High Negotiations Committee, told reporters it wants greater access for humanitarian aid and decried continued sieges by government forces on Syrian municipalities.
Mr Kerry’s meetings were arranged after Mr 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.
The other current significant difference between the US and Russia is the situation in Ukraine where Washington accuses Moscow of not doing enough to push pro-Russian separatists in the east to comply with a ceasefire.
Russia, meanwhile, has complained that the Ukrainian government is dragging its feet on implementing the ceasefire.
Mr Kerry was to raise concerns about a recent sharp increase in cease-fire violations and press Russia to do more to get the separatists in line. Unless there is “true quiet” and full access for ceasefire monitors, US officials say it will be difficult to get progress on other parts of the Minsk deal.
Mr Kerry will also raise the case of Nadezhda Savchenko, a Ukrainian pilot who was sentenced to 22 years in prison in Russia on Tuesday on charges the US says are false.