Officials of Hamas, which runs the Palestinian government, said they had agreed a truce with Fatah, loyal to Palestinian leader Mahmoud Abbas.
Fatah officials also spoke of a deal, but there were reports of heavy gunfire continuing into Sunday night.
Gaza City was wracked by fighting throughout the day, with two killed after Mr Abbas called for elections.
Hamas described the apparent deal as a “ceasefire to end the violence” between all armed Palestinian groups.
They said all armed men were being asked to get off the streets of Gaza and the West Bank.
The reports came at the end of a turbulent few days in the Palestinian territories.
Gaza City saw running street battles throughout Sunday: mortars were fired at Mr Abbas’s office in Gaza City, and a 19-year-old woman was killed as rival Fatah and Hamas supporters clashed in the streets.