"We cannot automatically move from one negotiation to another without written guarantees," Mussa, whose organisation backed indirect talks between Israel and the Palestinians in May, said.
Resuming direct talks
Ahmed Aboul Gheit, the Egyptian foreign minister, said after the meetings that no breakthrough had been achieved.
"We are still hopeful that we can bridge this gap. The gap between the needs for security for Israel and the borders for the Palestinians," he said.
Al Jazeera's Ayman Mohyeldin, reporting from Egypt, said that it looked as though the Palestinians would not be tempted back to negotiations without specific guarantees on crucial issues such as borders, settlements and security assistance.
"So far the indications are that not enough progress has been made to warrant moving from proximity talks to direct talks," he said.
In an interview with the Jordanian newspaper Al-Ghad on Saturday, Abbas laid out a number of conditions for negotiations with Israel. He said he would resume direct talks if Israel agreed to the borders prior to the 1967 Middle East war as the basis for a Palestinian state.
He also requested an international force deployed along the border to protect the Palestinian state.
"If they agree to that, we will consider that acceptable progress, and we will move to direct negotiations," Abbas told the newspaper.
Abbas made no mention of requiring Israel to freeze settlement growth, which has long been a precondition for direct talks. The 10-month suspension of new settlement activity in the occupied West Bank, announced last year by Netanyahu, will end in September.
Yasser Abd Rabbo, a senior Palestinian official, told Al Jazeera he wants the United States to clarify its position on several issues, including borders, before resuming direct talks.
Gaza disengagement plan
Looming over Sunday's meeting between Netanyahu and Mubarak was a proposal by Avigdor Lieberman, the Israeli foreign minister, to cut all ties with Gaza.
Lieberman leaked the proposal to the Israeli daily Yedioth Ahronoth, calling it a "second disengagement" from the Gaza Strip.
Israel would seal its land border with Gaza, and lift its naval blockade of the territory, while European countries would be asked to take the lead on reconstructing Gaza's economy, decimated by years of war and blockade.
The plan is unpopular with the Egyptian government, because it would force Cairo to take greater responsibility for Gaza.
Netanyahu has already sought to distance himself from the proposal, saying it had not received his approval.
"Policies on this matter are set by the prime minister and the cabinet... that's how it has always been, and that's how it will remain," an aide told the Israeli newspaper Haaretz.