By Nidal al-Mughrabi GAZA, Feb 4 (Reuters) - Mortar bombs exploded near the Gaza offices of Palestinian President Mahmoud Abbas on Sunday and rival gunmen exchanged fire in the streets, defying the latest truce in the factional war between Fatah and Hamas. Fierce fighting between Hamas and Fatah has brought life to a near-standstill for residents of the narrow coastal strip, home to 1.5 million Palestinians. A hospital official said two members of Abbas's presidential guard died on Sunday from gunshot wounds suffered in fighting over the weekend, raising to 27 the number of Palestinians killed in factional clashes in the last four days. Rival gunmen defied calls to withdraw from the streets, though both sides said they would abide by the truce. Hamas denied its gunmen fired mortar bombs near Abbas's office in Gaza. The explosions caused no injuries. More than 80 Palestinians have been killed in the fighting since December, when unity government talks between the ruling Hamas movement and Abbas's Fatah faction broke down and the moderate president called for holding new elections. Palestinians hoped a unity government would help ease a Western economic boycott of the Palestinian government. Senior officials from Fatah and Hamas factions agreed on Saturday to pull their gunmen off the streets of Gaza, but few checkpoints were removed by Sunday, and sporadic exchanges of gunfire continued overnight. Hours after the truce was announced by Interior Minister Saeed Seyam of Hamas, a member of Abbas's guard was killed and another was abducted on Saturday, security officials said. There was no official claim of responsibility for that shooting, which Fatah blamed on Hamas. Hamas denied involvement. Officials on both sides said further talks would be held on Sunday on implementing the terms of the truce. The fighting has increased pressure on the "Quartet" of peace brokers -- the United States, the United Nations, the European Union and Russia -- to make a fresh effort to revive Middle East peace talks. Islamist group Hamas took control of the Palestinian government last March after beating Abbas's secular Fatah group in parliamentary elections.