It was the bloodiest round of internal fighting in more than a year
Israel has allowed 180 members of a beleaguered clan loyal to Palestinian leader Mahmoud Abbas to enter its territory from the Gaza Strip.
The Fatah faction supporters ran to a border crossing after a day of bloody fighting with their bitter rivals Hamas, who control the territory.
An Israeli army spokesman said some had laid down their weapons as they approached the crossing.
The injured among them were sent to Israeli hospitals, he added.
Fatah and Hamas blamed each other for starting the fighting on Saturday, in which nine people were killed.
Reports say that the clashes broke out during a raid by Hamas on the stronghold of a local pro-Fatah clan.
Hamas had accused Fatah supporters of involvement in a bombing a week ago that killed five Hamas members and a young girl. Fatah denies this.
An Israeli border commander, Col Ron Ashrov, said the Fatah supporters were allowed in after a group including injured people and armed men ran up to the Nahal Oz crossing.
Fatah loyalists are security searched by Israeli border forces
When Israeli soldiers went to open the fence, they came under heavy fire, presumably by Hamas, he said.
The Fatah supporters were hand-cuffed and stripped for security screening as they crossed into Israel.
Col Ashrov counted 22 injured among them.
Israel opened the border after both Egypt and President Abbas asked for the Fatah supporters to be allowed in.
The office of Israeli Defence Minister Ehud Barak said Israel had agreed out of humanitarian motives.
Hamas fighters had tried to storm the family home of the Hilles clan in Gaza City on Saturday morning, using grenades and mortars, reports say.
A spokesman for the Hamas-run interior ministry accused the clan of hiding bombing suspects in its compound.
"The Hilles family has become a military force and members of the family have been attacking, abducting and even killing people," spokesman Ehab al-Ghasin said.
"We must put an end to their attacks on innocent citizens."
The family denies the allegation.
A clan leader and senior Fatah member Ahmed Hilles are among the people allowed into Israel.