Nimr Hammad, a political advisor to Abbas, said the president had told French Foreign Minister Alain Juppe that he had officially agreed to France's proposal to host a peace conference in Paris before the end of July.
Juppe raised the possibility of the conference during a visit to Israel and the West Bank last week.
"In order to start negotiations, their basis must be ending the Israeli occupation of Palestinian land occupied since 1967, and the borders of the state will be determined on this basis with land swaps agreed by both the Israeli and Palestinian sides," Nimr said.
After meeting Palestinian premier Salam Fayyad in Ramallah on Thursday, Juppe said France was willing to transform a scheduled meeting of international donors into a broader peace conference to help re-launch stalled negotiations.
"We would be prepared, on the basis of a request by the (Middle East) Quartet, to organize in Paris before the end of July, a conference that would not be simply for the donors but a broader political conference involving the negotiation process," he said.
Netanyahu not keen on negotiating with Hamas
Israeli Prime Minister Benjamin Netanyahu said on Sunday that his country was still considering its response.
"I heard the proposal brought by French Foreign Minister Alain Juppe and we very much appreciate our French friends and I will respond to them after we have considered matters. We will study the proposal and discuss it with our American friends as well ," Netanyahu told media at the beginning of Israel's weekly cabinet meeting.
He added that he would not consider resuming negotiations with any Palestinian government that includes the Islamist movement Hamas, which last month signed a unity deal with Abbas's Fatah movement, stating that Israel will not negotiate with an organization that seeks to destroy them.
France has welcomed a reconciliation deal between rival Palestinian movements Hamas and Fatah, despite Israel's vocal opposition.
Juppe is to head to the United States next week to promote France's plan, which has so far drawn a non-committal response from Washington, although it endorses President Barack Obama's call for talks based on the borders in effect before the outbreak of the 1967 Six-Day War, with agreed land swaps.
"We are in consultations with the parties and with the Quartet," State Department spokesman Mark Toner said on Friday. "I am not necessarily dismissing it."
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