US Secretary of State John Kerry met with Palestinian president Mahmud Abbas in Paris on Thursday for their second round of talks in two days.
The two men met for two hours with their teams in an upscale Parisian hotel, where Abbas hosted Kerry for dinner and late night talks on Wednesday, US officials said.
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.
There was no immediate comment on how the two days of talks went, but US officials have insisted they are making progress despite the tough issues to be resolved.
Little has trickled out about the details of Kerry's peace quest or what could be included in the framework to guide the talks going forward.
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".
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".
Israel is due to release a third tranche of Palestinian prisoners held for decades towards the end of March.
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Israeli army radio reported Wednesday 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.
"People who know me know that when I sink my teeth into something, if I get the bit between my teeth, I try to get it done," Maariv quoted him as telling the television station.
Kerry, who has pushed the two sides back to the negotiating table after a three-year gap, has no immediate plans to travel back to Israel after making 11 trips during his first year in office.
But he will likely meet early next month in Washington with Israeli Prime Minister Benjamin Netanyahu on the sidelines of an annual conference organised by a powerful American-Israeli lobbying group.
Leading Palestinian official Hanan Ashrawi told a visiting delegation from another American Jewish group that Israel was "wilfully sabotaging" Kerry's efforts particularly with its continued settlement building.
She argued that any peace deal must be founded in international law, and said that J-Street, one group which represents the Jewish American community, had "the dual challenge of influencing both the US administration and the hardline and extremist Israeli government; for there to be peace and stability, we must move rapidly".