His first stop on Sunday was to be Rome, where he will meet separately both Sergey Lavrov, Russian foreign minister, and Benjamin Netanyahu, Israeli prime minister.
Diplomats say negotiations on a UN resolution to revive Israeli-Palestinian peace prospects are making little headway, with Europeans waiting for a US response to proposals.
Jordan last month circulated a draft Palestinian text to the Security Council setting November 2016 as a deadline for the end of the Israeli occupation, AFP reported.
But the text ran into opposition from the US, which has veto power, and other countries that felt it lacked balance, diplomats said.
It was never put to a vote.
France stepped in last month to try to draft along with Britain and Germany a resolution that would win consensus at the 15-member council.
The Palestinians have said they would like a draft resolution to go to a vote before the end of the year.
France is also proposing to host an international conference to launch the new peace track.
Kerry met on Thursday with his French counterpart Laurent Fabius on the sidelines of climate talks in Lima, to discuss the tensions in the Middle East.