Kerry, on his tenth visit to the region since March last year, has said he remains "hopeful" that Israel and the Palestinians can achieve a deal in the short term, Israel's Ha'aretz daily reported.
He held talks with Abbas twice yesterday - first for six hours and then again for three hours - at the Palestinian leader's West Bank headquarters in Ramallah. The two leaders met again today to nudge forward the troubled peace process.
Amid deep mistrust, Israeli Prime Minister Benjamin Netanyahu first launched the tirade against Palestinian Authority President Abbas for welcoming Palestinian prisoners released by the Jewish state under the US-brokered deal.
"To glorify the murders of innocent women and men as heroes is an outrage," he said during a press conference with Kerry before the latter visited the West Bank town of Ramallah to meet Abbas yesterday.
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"If Mother Teresa was Chairperson of the Palestinian people and Montesquieu was the Chairman of the Parliament and Thomas Jefferson was president and Prime Minister and favoured a Palestinian state on the '67 borders and Jerusalem as its capital and resolving the refugee issue, our partners (Israel) would describe them as terrorists and say they should get rid of them," Erekat told Arabic newspaper Asharq al-Awsat.
"Prime Minister Netanyahu has serious, serious concerns about the plan that has been presented to him - whether it be the ability of Israel to defend its borders, the viability of a Palestinian state and their intentions and their actions toward the state of Israel, and particularly on the overall security," Senator John McCain told reporters here.
Kerry is now seeking to overcome concerns of the two sides about a "framework" to guide negotiations towards a lasting peace agreement.