The two leaders are believed to have discussed who might succeed Mr Abbas
Egypt's President, Hosni Mubarak, has called on Palestinian leader Mahmoud Abbas to stay in post and seek re-election in polls due next year.
Mr Mubarak urged him to "proceed with the national march in view of the Palestinians' dire need for his role" at talks in Cairo, a spokesman said.
The impasse in peace talks prompted Mr Abbas to decide not to run again.
The two leaders also discussed an Arab League plan to have seek UN recognition of an independent Palestinian state.
Earlier, the European Union described the proposal as "premature", saying it hoped one day to recognise a Palestinian state, but that such a state had to exist first.
The US acknowledged Palestinian frustration but also voiced opposition to the plan, saying negotiations were the way forward.
Israel has threatened to retaliate with unilateral measures of its own if the Palestinians take such a step.
During the talks at the presidential palace in Cairo, Mr Mubarak once again urged Mr Abbas to stay and run again in the forthcoming election, which is scheduled for January but may be delayed.
Saeb Erekat and Marwan Barghouti are possible successors to Mahmoud Abbas
The BBC's Christian Fraser in the capital says that while there was very little detail released to the media on what was said, there is no doubt the two men would have touched on who might succeed Mr Abbas as head of the Palestinian Authority.
Reports suggest Cairo is supportive of two people that have so far been put suggested - the chief Palestinian negotiator, Saeb Erekat, and the jailed Fatah leader, Marwan Barghouti.
Barghouti is currently in serving five life sentences an Israeli prison for murder, but he is still one of the most popular Palestinian leaders.
If there is no agreement on one particular candidate, then Cairo has hinted it might support joint leadership of the Palestinian Authority in the interim, our correspondent says.
Mr Abbas now heads to Jordan for talks with the French Foreign Minister, Bernard Kouchner, who has reiterated President Nicholas Sarkozy's comments on Tuesday that the current deadlock plays into the hands of the extremists.