Top aides to Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas began the talks over an iftar dinner - the evening meal with which Muslims break their daily fast during Ramadan - hosted by Kerry at the State Department.
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It was clear, however, from some public statements over the agenda for the talks - which are expected to run for nine months - and comments by Abbas, that there are major disagreements over issues such as borders and security.
The talks started over dinner with Israel represented by Justice Minister Tzipi Livni and Yitzhak Molcho, a close aide to Netanyahu, and the Palestinians by chief negotiator Saeb Erekat and Mohammed Ishtyeh.
Justice Minister Tzipi Livni said after the meeting, "We started out in a good atmosphere. Both sides want to move forward."
Addressing the decision to avoid leaks, she said, "The talks are discrete and no one wants to do any harm. If we're serious, and we are, we'll stick to it. In the past, we saw negotiations last for several months without any leaks by either side until the leak to Al-Jazeera."
"We all understand that once you start to play the blame game it only does damage. On a personal level, it was a meeting of old friends. We all spent many hours in the negotiating room together."
As the sides came together in Washington on Monday Kerry met separately with each, starting with the Israelis, before all came together around the dinner table. Kerry and his delegation of four, including new envoy Indyk, were seated on one side of the table and their guests on the other side, with the two main negotiators Livni and Erekat seated side by side.
The talks are set to resume on Tuesday at 3 pm (Israel time) at the State Department building. They will be overseen by US special envoy Martin Indyk and will discuss the outline, timetable and location of the talks. Secretary Kerry is set to join the parties two hours later. It is likely that the talks will be held in Israel or Jordan.
Speaking prior to the dinner, Livni said, "The aim is to bring an end of a years-long conflict between ourselves and the Palestinians. It sounds simple but it's in Israel's interest.
"It is not a favor to the United States or to the Palestinians, this is something that we need to do, but it's very complicated. We are setting out on a new path and we will have to see whether our goals are achievable."
On Monday, Palestinian President Mahmoud Abbas said that no Israeli settlers or border forces could remain in a future Palestinian state and that Palestinians deem illegal all Jewish settlement building within the land occupied in the 1967 Middle East war. He made the statements during a visit to Cairo.
Abbas also spoke to UN Secretary General Ban Ki-moon who had met with Livni and Attorney Yitzhak Molcho in New York before the two headed to Washington.
President Obama addressed the renewed talks earlier on Monday saying "This is a promising step forward, though hard work and hard choices remain ahead."
He further added, "The most difficult work of these negotiations is ahead, and I am hopeful that both the Israelis and Palestinians will approach these talks in good faith and with sustained focus and determination."
Reuters contributed to this report
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