In protest against attacks by militant supporters of President Mahmoud Abbas' Fatah, Hamas also closed all of its government ministries in the Palestinian territories.
In the northern West Bank town of Nablus, Deputy Prime Minister Nasser Shaer said Fatah militants shot at his bodyguards as they rode in a government car, injuring two of them. Shaer was not present during the attack. Hospital officials said a Fatah militant was also injured in the fighting.
At Gaza City's main hospital, a 20-minute gunbattle erupted when the family of one of those killed Sunday arrived to retrieve his body.
The Fatah gunmen accompanying the family opened fire on the Hamas militiamen patrolling the hospital, sending patients and doctors running for cover. No one was injured, hospital officials said.
Fatah also enforced a general strike in parts of the West Bank, closing shops and private schools in a show of force against Hamas.
Fatah militants also released a Hamas official in the Finance Ministry they had briefly kidnapped, telling him his abduction was intended to send Hamas a message to end the Gaza violence, Hamas officials said.
Speaking to his Cabinet on Monday, Prime Minister Ismail Haniyeh, of Hamas, said the tension in Gaza had eased, but worried about the West Bank.
"We reiterate to our people to be responsible, not to spread the circle of disagreements and conflict, and not to transfer events to other parts of the nation," he said.
The violence that killed eight people Sunday began when members of the Hamas-led government's 3,500-man militia confronted civil servants, including members of the Fatah-allied security forces, who were protesting the government's inability to pay their wages.
The tense confrontations erupted in running gunbattles that spread across the Gaza Strip, sending civilians fleeing for their lives and turning the center of Gaza City into a battle zone.
Fatah militants quickly followed through on a promise to retaliate for the Gaza violence with attacks of their own in the West Bank, where Hamas is far weaker.