The first session of talks ended last night with no immediate progress reported.
The task facing Mr Peres and Mr Abbas remains considerable. Israel's withdrawal from the Gaza Strip and Jericho area was meant to have begun on 13 December. But the two sides could not agree on what constitutes the Jericho area, and who should control access to the two enclaves.
On Sunday, the Israeli Prime Minister, Yitzhak Rabin, told his cabinet at its weekly meeting that Israel was prepared to double the size of the 'Jericho area'. Despite this concession, Mr Peres went into yesterday's talks saying he had nothing more to offer the PLO chairman, Yasser Arafat.
'I hope very much that Arafat will climb down from his tree, because I am not bringing anything new,' Mr Peres, who is usually optimistic, told the newspaper Yedioth Ahronoth.
Israel is unwilling to renounce any control over borders into the new enclaves, lest those allowed in would then more easily be able to enter Israel. Cabinet ministers are united in stressing that there would be no compromise on Israel's security.
Despite the delay, Mr Peres was hopeful that the accord would be implemented. 'If it takes a day, two days, a week, two weeks, if it takes a month or two months, we will stand by our principles,' Mr Peres told parliament yesterday. Hours later, the government defeated no-confidence motions by 54 votes to 44.
Mr Peres, frequently interrupted by heckling from opposition members, said Palestinians would not receive the 300 sq km (115 sq miles) they wanted around Jericho, and the area would not stretch to the Dead Sea.
The lack of progress in the talks, the absence of real change on the ground, and Mr Arafat's authoritarian and personal leadership style, have all helped to aggravate tensions within the ranks of his mainstream Fatah movement.
At least four senior Fatah officials in the Israeli-occupied territories resigned at the weekend, in a challenge to Mr Arafat at a time when he needs to marshal maximum support for the accord.
'The Palestinian negotiations are being run the wrong way,' said Sami Abu Samhadana, chief of Fatah's Gaza Strip office, who resigned along with Jamal al-Dik, a senior West Bank Fatah leader.
The sources said two other Fatah leaders had also resigned. They were Tawfik Abu Khousa, Abu Samhadana's deputy and Fatah delegate to the Unified Command of the Intifada (Palestinian uprising), and Zakharia Talmas, head of the Gaza Arab Journalists Association.
Many younger Fatah leaders in the occupied territories felt that Mr Arafat favoured fawning, wealthy traditional figures - 'a salon leadership' - over activists who had led the intifada and paid dearly in prison for their activities.
A central issue was Mr Arafat's decision last month to name two old-line leaders, Faisal al-Husseini and Zakharia al-Agha, to head Fatah's organisation in the West Bank and Gaza respectively.
The PLO-Israel accord is only one part of the comprehensive settlement which is sought through negotiations by Israel with its Arab neighbours. Yesterday, the Syrian Foreign Minister, Farouk al-Sharaa, arrived in Amman to co-ordinate policy with King Hussein of Jordan in advance of the summit between President Bill Clinton and Syria's President Hafez al-Assad in Geneva on 18 January. Jordan is all but ready to sign a full agreement with Israel, but will only do so in concert with Syria. President Assad, who plays a long hand, is waiting to see how the PLO-Israel accord works in practice before committing himself.