"Kerry is exerting strenuous efforts... To come to a solution" to the Israeli-Palestinian conflict, Abbas told a news conference in Ramallah.
"I believe the ball is now in Israel's court.
"The Palestinian demands are clear, and the Israelis know them as do the Americans, so Israel must now accept them in order to begin negotiations," said Abbas.
Palestinian demands for a return to talks, which stalled in September 2010, include an end to Israeli settlement building in the West Bank and annexed east Jerusalem.
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Palestinian chief negotiator Saeb Erakat said today: "All I want to do now is to focus on how to make Kerry succeed. I don't want to speculate on his failure."
Israel and the Palestinians are at odds particularly over settlement building -- a key issue that led to the failure of talks in 2010 -- especially given the ardent pro-settlement stance of some members of the current Israeli cabinet.
The visit would be the top US diplomat's first since the appointment of Palestinian prime minister Rami Hamdallah, whose predecessor Salam Fayyad resigned in April.