The armed confrontations in Gaza on Saturday, which wounded 20 people, followed condemnation by Khalid Mishaal, the exiled leader of Hamas, of Mahmoud Abbas, the president who heads the Fatah group. President Abbas had vetoed the formation by Hamas of a new Gaza security force.
Mahar Meqdad, the Fatah spokesman, said on Sunday: "The two parties have agreed to call on our people to stop all forms of tension and to cement national unity." He was speaking after a meeting between the two groups, mediated by Egyptian officials.
Officials from the groups did not elaborate on what practical steps would be taken on the ground to stop violence.
Sami Abu Zuhri, the Hamas spokesman, said: "Internal orders were given to guarantee there would be no return to friction." He said that a joint Hamas-Fatah committee would be formed to discuss how to handle any future disputes between the groups.
The appointment of Jamal Abu Samhadana, head of the Popular Resistance Committees, which has often attacked Israel, as leader of a new Gaza police force was widely seen as an attempt by Hamas to strengthen its grip on the interior ministry.
"The two parties have agreed to call on our people to stop all forms of tension and to cement national unity"
Abbas vetoed the decision. Mishaal said Abbas's move assisted a Western campaign to isolate the Palestinian government.
Students and militants loyal to Hamas or to Fatah took to the streets, exchanging gunfire in Gaza and wounding 20 people.
Chanting "Mishaal is a traitor", thousands of Fatah loyalists marched in Gaza, some firing rifles in the air. Many also protested in the West Bank.
Mishaal said after the violence on Saturday that Hamas respected Abbas's authority and called for Palestinian unity, saying: "We were united during the [uprising] in confronting the Israeli occupation. Today we have to be united in politics."
The interior ministry said the new Gaza force would work from within the existing security establishment, headed mainly by Fatah loyalists, but Abbas's aides said only the Palestinian president could make decisions regarding the government.
Abbas vetoed the appointment
of a Hamas leader as police chief
Lawlessness by rival armed groups has increased in Gaza Strip in recent years, but Hamas and Fatah had rarely engaged in violent confrontations.
Hamas, a militant group sworn to destroying Israel, beat Fatah in an election in January to head the Palestinian government.
Hamas carried out about 60 suicide bombings during an uprising in 2000, but has largely abided by a truce since last year.
Ghazi Hamad, the cabinet spokesman, said aides to Abbas and Ismail Haniya, the prime minister, would meet to try to solve the Gaza security dispute before a meeting between the leaders this month when Abbas returns from a visit abroad.