Abbas, who arrived in Gaza to reinforce the ceasefire punctured by a new wave of violence, said abiding by the calmness was in common interests for all Palestinian factions including the Islamic Hamas and Jihad.
The Palestinian president also condemned Israeli troops' aggressions against the Palestinians, warning that an escalation of Israeli military actions might destroy the ceasefire.
An unmanned Israeli army drone fired on Wednesday two missiles at three Hamas militants who attempted to launch rockets on Jewish settlements near the southern Gaza town of Kahn Younis. The militants escaped unharmed.
The incident came as Palestinian militants stepped up rocket attacks on Israel and Jewish settlements in Gaza and Israeli troops clashed with militants, leaving several dead.
The new flare-up has posed a grave challenge to the de facto truce that Palestinian militants committed themselves to at the behest of Abbas.
Israel has repeatedly demanded the Palestinian leadership to rein in militants as a planned withdrawal from Gaza and the northern West Bank will come in just two months' time.
Meanwhile, Hamas spokesman Sheikh Hassan Yousef said Abbas told a Hamas delegation in the West Bank city of Ramallah shortly before he headed to Gaza that he will return a heatedly-debated new electoral law to the Palestinian Legislative Council (PLC) for approval.
After the PLC okays the amended law draft, Abbas said he will set a new date for the parliamentary elections based on the consensus of all Palestinian factions, Yousef added.
Ibrahim Abul Naja, head of the Follow up Committee of the National and Islamic factions, said Abbas will hold several meetings with Hamas and other factions to try to remove disputes caused by the postponement of the legislative elections.
Earlier this month, Abbas decided to postpone the elections originally scheduled on July 17 to allow more time to settle his disagreements with the PLC over the new electoral law which is to oversee the ballot.
The delay has sparked opposition from the Islamic Hamas, which is set to show a strong performance in its first parliamentary election bid.