The New York Times noted Saudi Arabia, until now, has remained out of internal Palestinian affairs.
"I call on my brothers, the Palestinian people, represented by their leaders, to put an immediate end to this tragedy and to abide by righteousness," Abdullah said in an announcement reported by the official Saudi Press Agency.
The Palestinian news agency WAFA said the talks are to take place on neutral ground in the holy city of Mecca.
Abdullah has reportedly said internal Palestinian fighting could jeopardize efforts to create a Palestinian state.
"Unless the wise in Palestine put a decisive and immediate end to the dispute ... it would deny the steadfast Palestinian people any hope in ridding itself of the hell of the Israeli occupation and (block) the creation of an independent free state of Palestine," WAFA quoted him as saying. "What is happening in the land of brotherly Palestine serves only the enemies of the Islamic and Arab nations and puts question marks in the minds of the international community which respects our just (Palestinian) cause."