Israeli and Palestinian officials held talks in Jerusalem on Tuesday and were to meet again later the same day, Palestinian sources said, just six days after they resumed direct negotiations.
An initial two-hour meeting took place in secret in the morning, with negotiators set to return to Jerusalem's King David Hotel for a "second round of talks" at around 7:30pm (1630 GMT), a senior official said on condition of anonymity.
"A meeting was held today between the Palestinian delegation, headed by Saeb Erakat and Mohammad Shtayyeh, and the Israeli delegation of (Justice Minister) Tzipi Livni and Yitzhak Molcho," the official told AFP, saying the talks had started at 11:00 am (0800 GMT).
The meetings were taking place just six days after Israeli and Palestinian negotiators formally resumed direct peace talks after a hiatus of nearly three years, thanks to an intense bout of shuttle diplomacy by US Secretary of State John Kerry.
Details of the morning discussions were not revealed, following a request from Washington last week for a strict news blackout.
The latest bout of talks were to have taken place in the West Bank city of Jericho on Wednesday, but had to be pulled forward due to a planned visit by Erakat to Russia.
Ahead of the meeting, Kerry's special envoy Martin Indyk on Monday met Palestinian president Mahmud Abbas to keep up the pressure to continue talking "despite continued settlement building, which is the biggest obstacle to talks carrying on," the official said.
Although the Palestinians had pushed for further US pressure on Israel at the talks, the Israeli side insisted that Tuesday's meetings take place without US involvement, he said.
In the evening, the negotiators were to focus on "how to begin discussing borders and security," one source said, indicating that the talks on borders would touch on the issue of Jerusalem, settlements and the Jordan River.
Each team was expected to hand over a list of names of the negotiators who would chair committees on key issues such as Jerusalem, borders, security, prisoners, water , settlements and the economy.
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"The Palestinians already have their list of names, they just need the list from the Israelis," he said.
The negotiators will meet again next week in Jericho although no date has yet been set.
The opening round of talks, held in Jerusalem on August 14, were held under a shroud of secrecy at an undisclosed location in Jerusalem.
Abbas said all they key issues were discussed but declined to elaborate.
But the long-awaited return to peace talks was overshadowed by a new row over Israeli settlement plans for the occupied Palestinian territories.
In the days leading up to the talks, Israel announced plans to build more than 2,000 new homes for Jewish settler in annexed east Jerusalem and the West Bank, enraging the Palestinians.
Speaking in Ramallah a day after the talks began, UN chief Ban Ki-moon told reporters he was "deeply troubled by Israel's continued settlement activity in the West Bank, including east Jerusalem.
"Settlement activity is deepening the Palestinian people's mistrust in the seriousness on the Israeli side towards achieving peace. It will ultimately render a two-state solution impossible," he warned.
But Israel's Prime Minister Benjamin Netanyahu played down the issue when he met with the UN leader the next day.
"The root cause (of the conflict) was and remains the persistent refusal to recognise the Jewish state in any boundary," he said on Friday.
"It doesn't have to do with the settlements - that's an issue that has to be resolved, but this is not the reason that we have a continual conflict."
Peace talks broke down just weeks after they began in September 2010 over the issue of settlement building.