Witnesses said there was no sign of any armed members of either group on roads in several militant stronghold towns in northern Gaza.
Hamas militants and forces from the ruling Fatah faction fought gunbattles in the Gaza Strip today, wounding 13 people.
Egyptian officials, working with Israel and the Palestinian Authority to coordinate the Jewish state’s planned withdrawal from Gaza in August, had mediated during the day to try to end the fighting.
The clashes erupted after two Hamas offices and a vehicle were torched in attacks that Hamas and Fatah blamed on each other.
Palestinian security forces said they had tried to stop Hamas, an Islamist group sworn to Israel’s destruction, from firing rockets into the Jewish state.
The clashes occurred in the Jabalya refugee camp while Mr Abbas was in nearby Gaza City.
Mr Abbas had earlier warned militants he would not tolerate further fighting with his security forces or attacks on Israel.
Clashes between the two sides last week had raised fears among ordinary Palestinians of civil war.
Hamas, which has posed a growing challenge to Abbas, said it had resumed firing mortars at Jewish settlements in Gaza after a lull, calling them responses to Israeli military actions.
Israel and the United States have been pressing Mr Abbas to rein in gunmen.
Before the clashes, he had largely preferred to negotiate with the armed groups, prompting them to accept a truce he had declared with Israel.
Militants have stepped up rocket and mortar bomb attacks against Jewish settlements since a series of Israeli air strikes killed seven Hamas gunmen last week. The air strikes followed a deadly Palestinian suicide bombing.