(Adds more quotes, background) RIYADH, Jan 28 (Reuters) - Saudi Arabia invited feuding Palestinian leaders for urgent talks in Islam's holy city of Mecca and both the Hamas-led Palestinian government and rival faction Fatah said on Sunday they had accepted the offer. The invitation from Saudi King Abdullah was announced on the third day of fierce clashes between Palestinians in Gaza in which 23 people have been killed, heightening fears of civil war. "I invite them all ... for an urgent meeting in brotherly Saudi Arabia at the sacred house of God (Mecca's Grand Mosque) to discuss disputes in a neutral (environment) without intervention from any other side," the official Saudi Press Agency (SPA) quoted Abdullah as saying in an open letter. The Islamist militant group Hamas won Palestinian elections a year ago, unseating President Mahmoud Abbas's once dominant Fatah. "We welcome the invitation by His Majesty King Abdullah and the government appreciates this generous position, which comes in an attempt to resolve Palestinian internal differences," Palestinian Foreign Ministry spokesman Taher An-Nono said. A senior Fatah official also said the group welcomed the invitation and was ready to participate in the talks. Abbas and Hamas politburo chief Khaled Meshaal met in Damascus earlier this month to iron out their differences, but said they needed to hold further talks. Abdullah, who proposed an Arab-Israeli peace initiative adopted at an Arab League summit in 2002, said inter-Palestinian fighting could jeopardise 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 Zionist (Israeli) occupation and (block) the creation of an independent free state of Palestine," he said. "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." Abdullah said the invitation was based on an Islamic rule that Muslims must solicit rapprochement if fighting erupts among followers of the faith. "The government and people of Saudi Arabia do not accept to stand silently and watch with deep sorrow and pain as brothers, who share a cause, fight ... our hearts bleed," he said. (Additional reporting by Mohammed Assadi in Gaza)