The two men met today for two hours with their teams exchanging Abbas's Ramallah headquarters where they normally meet for an upscale hotel where the Palestinian leader also hosted Kerry for dinner yesterday.
The top US diplomat has spent months trying to get the Israelis and the Palestinians to agree on a framework for resolving their conflict, but the negotiations have shown little sign of progress, with each side blaming the other.
"As they did last night, they discussed all of the core issues and agreed to stay in close touch over the phone and through their teams on the ground in the coming days and weeks," the official added.
Palestinian ambassador to Paris, Hael al-Fahum, told Voice of Palestine radio that Abbas "had outlined his vision of a peace which is based on international law".
More From This Section
The Palestinian leader also insisted there could be no deal without east Jerusalem as the capital of a state of Palestine and "a resolution of all the issues, in particular security, refugees and the release of prisoners".
Israeli army radio reported yesterday that Washington was to demand that Israel implement a partial settlement freeze after Kerry presents his framework.
According to the Israeli daily Maariv, Kerry alluded in an interview with Channel 2 television to the possibility that some settlers who live in areas earmarked for Palestinian sovereignty may not have to leave their homes in a final peace deal.
And despite the tough talks and a barrage of personal attacks he was determined to stay the course, Kerry told the television.