"We reached understandings on almost all of the points, and needed to do a summary," Peres told Channel 2 in an interview in which he said that he held a series of meetings with Abbas at that time.
The Nobel laureate Israeli President cancelled the last meeting at Netanyahu's instructions.
The prime minister had the impression that Quartet envoy Tony Blair would be able to bring a better offer, elder statesman Peres said.
The Israeli President, who is in the final months of his tenure, claimed that his Palestinian counterpart was willing to recognise Israel as the Jewish state in return for the establishment of a Palestinian state.
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Regarding the other core issue of absorbing Palestinian refugees, Peres said that an agreement was reached along the lines of the Arab League initiative that the problem would be resolved in an agreed and just manner.
He emphasised that the meetings with Abbas, held at a time when there were no negotiations, were conducted with Netanyahu's knowledge and consent.
Sources in the Prime Minister's Office denied that Abbas agreed to anything at the time, and that, as is the case now, "all he wanted was to take from Israel without giving anything in return," the Jerusalem Post reported.
The only agreements that Abbas has made were "ones with Hamas", the sources were quoted as saying.
In reference to Abbas' meeting in Qatar on Monday with Islamist Hamas head Khaled Mashaal, the sources reportedly said that "anyone who embraces the arch-murderer Mashaal" does not want peace with Israel.