Israeli air strikes in the West Bank and Gaza have killed at least five Palestinians, four of them militants from the Hamas organisation.
At least two Hamas members died in the air strike in Gaza city
Earlier, clashes in Gaza between Palestinian Authority forces and Hamas members killed two bystanders.
US Secretary of State Condoleezza Rice is to visit the region next week amid appeals to both sides to restore calm.
The surge in violence comes just one month ahead of Israel's planned disengagement from Gaza.
Reports quoting Palestinian security sources say two Hamas leaders were killed by rockets from Israeli helicopters near the northern West Bank town of Salfit.
Hamas supporters set fire to a Palestinian police armoured vehicle
Rabih Harb and Mohammed Ayash, were travelling in a car through an industrial area of the town. They were members of the armed wing of Hamas, the Ezzedin al-Qassam Brigades.
There was no immediate comment from the Israeli army.
At least three Palestinians were killed in east of Gaza City after a missile hit a van. Hamas said two of the men were its members.
Medical sources say five civilian bystanders were also injured.
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.
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.
One the Israeli missiles struck an Islamic centre in Jabaliya
Reports say that the bystanders killed in the fighting were a teenager and child.
The Palestinian violence began on Thursday evening. Palestinian Authority security forces opened fire on a car carrying Hamas members, injuring several militants.
The US State Department has said Condoleezza Rice will meet Israeli and Palestinian leaders next week to try to stop the violence spiralling.
"We're closely engaged with both sides and we encourage them to take appropriate steps to restore order and calm," said State Department spokesman Sean McCormack.
The BBC's State Department correspondent Jonathan Beale says this will be Condoleezza Rice's third trip to Israel and the Palestinian territories in the space of five months, and it is a sign of increasing concern in the United States that Israel's planned withdrawal from Gaza could be disrupted because of the violence.
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.