Clashes in Gaza between Palestinian Authority security forces and members of the Hamas militant organisation have killed two bystanders and injured 20.
Hamas supporters set fire to a Palestinian police armoured vehicle
The fighting in Gaza City started on Thursday and continued into Friday morning before appearing to die down.
On Thursday night, Israeli helicopters fired missiles at three targets in the Gaza Strip.
The strikes came after a woman in Israel was killed by a rocket fired from the Gaza Strip on Thursday.
The al-Aqsa Martyrs' Brigades and Hamas said they carried out Thursday's rocket attack, in response to the killing of an Islamic Jihad leader by the Israeli army in the West Bank town of Nablus.
Palestinian leader Mahmoud Abbas has gone to Gaza to hold talks with armed groups, in an attempt to put an end to militant attacks.
BBC Gaza correspondent Alan Johnston says that the Palestinian leadership appears to have launched a concerted effort to exert its authority by force.
One the Israeli missiles struck an Islamic centre in Jabaliya
There are reports of Palestinian security forces coming under fire from rocket-propelled grenades and sporadic bursts of gunfire could be heard on Friday morning.
Private cars blaring their horns raced through the city carrying the injured. But the situation is now reported to be calmer in the Zeitoun area of Gaza City, with the Palestinian Authority units having apparently pulled back.
In some of the worst violence between Palestinians in recent years, Hamas militants set fire to a police station, a police armoured personnel carrier and three jeeps.
Thick black smoke from burning tyres rose from the area.
Reports say that the bystanders killed in the fighting were a teenager and child.
The violence began on Thursday evening. Palestinian Authority security forces opened fire on a car carrying Hamas members, injuring several militants. Hamas counter-attacked, targeting the police station in the area.
The militants in the car had been on a mission to launch missiles at a nearby Israeli target.
Mr Abbas has been under intense Israeli and Western pressure to try to halt such rocket attacks.
Thursday's fatal rocket attack was the first in Israel since February
Our correspondent says he has always been very reluctant to use force, but pressure to take decisive action grew after the Israeli woman was killed by a missile fired from Gaza.
His administration has now said that it is determined to take firm measures to impose order.
Violence escalated on Tuesday, when an Islamic Jihad militant killed five Israelis in a suicide bombing in the Israeli coastal resort of Netanya. Israel responded by carrying out raids in Nablus. This in turn triggered Thursday's rocket attacks by al-Aqsa Martyrs' Brigades and Hamas.
Soon after the rocket attacks, Palestinian police, reportedly acting on orders to stop further rocket fire, clashed with Hamas members in northern Gaza.
Israel has occupied Gaza and the West Bank since 1967.
Israeli disengagement from Gaza is due to begin in August.
Approximately 8,500 settlers and the soldiers that protect them are due to be withdrawn from Gaza. Israel will maintain control over Gaza's borders, coastline and airspace.
About 630 settlers will also be removed from four small West Bank settlements.