Negotiators were holding peace talks in Jerusalem on Monday, Palestinian officials told AFP, although Israeli sources refused to confirm the meetings.
Meetings between the two sides, launched in Jerusalem in August, have been mostly held in secret under a US-requested media blackout, and the Palestinian sources declined to be identified.
During a flying visit on Sunday focused on the Syria conflict, US Secretary of State John Kerry held talks in Jerusalem with Israeli Prime Minister Benjamin Netanyahu.
Kerry kept his remarks on the peace talks to a minimum.
"We are convinced that the best way to try to work through the difficult choices that have to be made is to do so privately," he said. "We will not discuss the substance of what we are working on."
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Palestinian president Mahmud Abbas, meanwhile, a week after meeting Kerry in London, rejected the notion of an Israeli military presence in the Jordan Valley of the West Bank under any final-status agreement.
"The security of the (future) Palestinian state's borders are the responsibility of Palestinian security forces first and foremost," he told reporters in the West Bank city of Jericho.
Israel demands a long-term Israeli military presence in the Jordan Valley in case a Palestinian state is established.
Security and Jewish settlement building on Palestinian land are two of many contentious issues which have led to the collapse of peace talks in the past.
Abbas called on the European Union to enforce guidelines it published in July that would ban its institutions from dealing financially with or funding any Israeli settlements in the West Bank from 2014.
Kerry last week urged the EU to suspend the guidelines.
"I did ask the European community if they would consider a suspension," he said. "It's not asking them to change the policy, it's asking them to suspend or delay its implementation while these talks are taking place."