Netanyahu wants Mubarak to push Abbas to restart direct talks with Israel.
But expectations are low. Direct talks have been stalled for more than a year over a number of issues, particularly the continued growth of Israeli settlements in occupied East Jerusalem and the West Bank.
Resuming direct talks
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 1967 borders 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 West Bank settlement freeze 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
One issue likely to loom over Sunday afternoon's Netanyahu-Mubarak meeting is 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. 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.