Story Highlights• Egyptian officials broker truce between Hamas and Fatah
• All checkpoints to be dismantled under the agreement
• Four militants died Sunday in fighting between the rival groups
• Sources: Fatah militants kidnapped a professor who has ties to Hamas
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(CNN) -- Hamas and Fatah began observing a cease-fire early Monday, officials from both sides said.
"In order to maintain national unity and preserve Palestinian blood, Hamas and Fatah leaders met and agreed to end the fighting and remove the checkpoints," Ayman Taha, a Hamas official, said.
Under the agreement, gunmen from the rival factions were ordered off the streets and any hostages being held were to be released.
The truce, brokered by Egyptian mediators, Taha said, was to begin at 1 a.m. (6 p.m. Sunday ET).
Earlier Sunday, violence between Hamas and Fatah raged in Gaza, leaving four militants dead and several others wounded, Palestinian sources said.
Two Hamas militants died in a firefight with Fatah militants outside a mosque in Gaza City, Palestinian security sources said.
Nine other Palestinians -- four Hamas militants and five bystanders -- were wounded, the sources said.
In a separate incident, a commander of Fatah's armed wing, the Al Aqsa Martyrs Brigades, and his assistant were shot to death by an unknown gunman in northern Gaza, according to security sources.
Fighting then broke out at the commander's funeral in Jabalya, but there were no immediate reports of casualties.
Security sources also said Fatah militants kidnapped Ali Sharif, a professor at the Islamic University of Gaza who has ties to Hamas.
Hamas claimed in a leaflet that it has kidnapped 70 Fatah members, Hamas sources said. Fatah did not immediately confirm the claim.
Last year, Hamas ended decades of Fatah rule by winning Palestinian elections. Hamas took control of the parliament and the prime minister post, although Fatah's Abbas maintained the title of president.
After months of deadly clashes, the two sides met recently to build a new government aimed at ending the fighting.
Both Hamas and Al Aqsa have carried out numerous terrorist attacks against Israel.
The U.S. State Department has designated both Hamas and Al Aqsa as terrorist organizations.
CNN's Waffa Munayyer contributed to this story