By Nidal al-Mughrabi GAZA, June 12 (Reuters) - Palestinian gunmen fired a rocket-propelled grenade into Prime Minister Ismail Haniyeh's Gaza home on Tuesday, causing damage but no injury as factional fighting raged for a fourth day, officials said. Haniyeh of the Islamist Hamas group was unharmed in the attack, the latest incident in intensive clashes that have cast the gravest of doubt on the future of a unity coalition he forged with President Mahmoud Abbas's Fatah faction in March. Fawzi Barhoum, a Hamas spokesman, accused Fatah of firing the rocket in an attempt to assassinate Haniyeh and vowed punishment "without mercy" of the perpetrators. There was no immediate comment from Fatah. The grenade "penetrated the house and exploded", Barhoum said. "Thank God there are no injuries," he added, confirming that Haniyeh was inside at the time but unharmed. "Hamas has decided to punish the attackers and the killers and it will not be reluctant to punish them without any mercy." It was the second time since Monday that Haniyeh had come under attack, including a shooting at his office on Monday that interrupted a cabinet meeting, but caused no casualties. Fourteen people were killed in fighting on Monday, including a woman who died of injuries early on Tuesday, hospital officials said, raising the toll since the latest round of fighting began on Saturday to 20. Gunmen from both groups continued to trade fire on the streets of Gaza City and the northern Gaza Strip early on Tuesday, witnesses said. Militants also renewed rocket attacks on southern Israel, and one injured an Israeli in the town of Sderot, close to Gaza, an Israeli medic said. The death toll in Monday's fighting was one of the highest in the internal strife, in which some 630 Palestinians are estimated to have been killed since Hamas beat Fatah in an election 18 months ago. The fighting doomed an Egyptian-brokered ceasefire announced in the morning and cast a shadow over long-term prospects for the coalition that Hamas and Fatah formed three months ago in an effort to ease tensions.