Aljazeera's correspondent reported Abbas was holding talks with the Committee for Palestinian National and Islamic Forces at the Gaza headquarters of the Palestinian Authority.
Representatives of the Islamist movements Hamas and the smaller Islamic Jihad are among those attending Thursday's meeting.
Aljazeera reported the meeting will discuss two key issues.
The first is the postponement of legislative elections recently announced by Abbas and the second is to maintain calm in the Palestinian territories.
Abbas travelled to Gaza in the aftermath of an attack, claimed both by Hamas and Islamic Jihad, on a Jewish settlement which killed two Palestinians and one Chinese farm worker.
Tension was stoked on Wednesday when four Hamas followers escaped an Israeli air strike on their vehicle.
The factions have been observing a less than watertight truce since January but say they reserve the right to respond to "Israeli aggressions".
Hamas claimed responsibility for
an attack on a Jewish settlement
The moderate Palestinian leader has consistently called for an end to the armed uprising, now nearly five years old, but has held back from meeting Israeli demands to launch a formal crackdown on the likes of Hamas.
Palestinian sources said that Abbas would also seek to explain his recent decision to indefinitely postpone parliamentary elections, originally scheduled for next month.
An explosion rocked a refugee camp in the Gaza Strip on Thursday, witnesses said.
There were no immediate reports of injuries.
The Israeli army denied involvement and said the blast appeared to have been an accident. During more than four years of fighting with Israel, dozens of Palestinian fighters have died while mishandling explosives.
Palestinian security officials could not immediately be reached for comment.
In the West Bank, residents of the Palestinian town of Salfit organised a demonstration in protest against the building of the barrier wall.
Israeli forces fired tear gas at demonstrators to prevent them from advancing toward land seized to build the wall.