Rawhi Fattouh, a senior aide of the president, said after talks between Palestinian factions late on Saturday in Gaza that the groups were close to finalising an agreement on a political platform, saying, "maybe Monday's session will be the final session".
Fattouh and Ismail Haniya, the Palestinian prime minister and Hamas leader, said more talks were needed regarding three points mentioned in the proposal. Officials from both groups refused to give details on the issues discussed.
"There are still some points remaining that need more consultations," Haniya said. "God willing, in the very near future, our people will listen to something assuring."
Abbas had said earlier on Saturday during a Cairo visit that an agreement on a political platform by the groups, caught in a violent power struggle, would mean there would be no need for a July 26 ballot on a proposal that implicitly recognises Israel.
He also promised to continue a 16-month-old ceasefire with Israel - denying Hamas ever broke it.
After meeting Hosni Mubarak, the Egyptian president, on Saturday, Abbas said Hamas had not discarded the truce in the past week.
"Hamas did not terminate the period of calm, although minor violations have happened, due to the killing of the family [on a Gaza beach on June 9]," he said.
The Palestinian leader promised to uphold the ceasefire "in order to have people living in peace".
Abbas (R) had thrown his weight
behind a political referendum
His comments came two days after Hamas, which holds a majority in the Palestinian parliament, offered to restore the truce, which broke down after a beach explosion killed eight Palestinians, including women and children.
Israel was shelling Gaza around that time but has said it was not responsible for the beach blast.
Israel responded favourably to the offer by Hamas.
Mark Regev, spokesman for Israel's foreign ministry, said on Friday that "if it is quiet, we will answer that with quiet".
But violence has since resumed.
An Israeli air raid late on Friday against suspected rocket launchers in Gaza killed two Palestinian fighters, Israeli and Palestinian officials said.
Earlier, Palestinians had fired five homemade rockets into Israel.
Although the rockets were not fired by Hamas, they were likely to endanger prospects for a return to quiet following days of intense bloodshed.
An Israeli air raid in Gaza on
Friday killed two Palestinians
In Egypt, Abbas also talked to Mubarak about infighting between his Fatah party and the ruling Hamas, with Mubarak underscoring the need for continued dialogue between the two factions, said Mubarak's spokesman Suleiman Awwad.
"The dialogue will yield results that are in harmony with international legitimacy, and will prove to the world that there is a Palestinian partner who is worth resuming negotiations with," Awwad said.
Abbas also thanked Egypt for humanitarian aid sent to the Palestinian territories.
After Mubarak met Ehud Olmert, the Israeli prime minister, in Sharm al-Sheikh on June 4, more than 50 truckloads of Egyptian medicine and food were allowed to cross into Gaza, Awwad said.