Mr Kerry is due to hold urgent talks on the situation with the UN envoy to Syria, Staffan de Mistura, and the Saudi and Jordanian foreign ministers.
A top priority, he said, was ending the violence in the northern city of Aleppo.
More than 250 civilians have been killed in Aleppo in the last 10 days.
A Russian defence official said earlier that negotiations were taking place to establish a ceasefire there.
The US wants Russia to put pressure on its ally the Syrian government to stop what it says is indiscriminate bombardment.
The Russian and Syrian governments say the Aleppo strikes are targeting the Nusra Front - a jihadist force not party to a ceasefire agreed in February.
Syria Aleppo: Kerry begins new bid to stop fighting
02 May 2016
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US Secretary of State John Kerry is in Geneva in an attempt to bolster a fragile, partial ceasefire in Syria.
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