Buildings have been reduced to rubble in the attacks
Helicopters and F-16 jets attacked a number of buildings in Gaza City, including a compound used by Palestinian leader Yasser Arafat.
The air raids took place as the American envoy to the Middle East, Anthony Zinni, met Israeli Prime Minister Ariel Sharon to seek an explanation for Israel's decision to sever all contacts with Mr Arafat.
Mr Zinni is expected to make an announcement later on Friday about the next steps he plans to take in his attempts to curb violence in the region.
The latest strikes followed helicopter attacks on targets in the West Bank in which a police station in Ramallah and offices of Mr Arafat's Fatah faction in Jenin were hit.
Israeli tanks had already entered Ramallah and taken up positions close to Mr Arafat's headquarters, while sappers destroyed a nearby television and radio centre.
BBC Middle East correspondent James Reynolds says the strikes have a clear aim - to destroy Palestinian Authority institutions.
Mr Sharon's government has said it will deploy its forces in the West Bank and Gaza in order to carry out arrests and confiscate weapons, as it does not believe Mr Arafat is doing enough to control militant groups.
Palestinian officials insist they are doing all they can in difficult circumstances, and say it is difficult for their police force to arrest militants while their police stations are being bombed.
The Israeli move to sever ties with Mr Arafat followed an attack by Palestinian militants on a bus on Wednesday, which left at least 10 Jewish settlers dead.
Both the US and European Union have said that they will continue to deal with Mr Arafat.
At least four Palestinians died on Thursday and about 20 others were wounded.
A Palestinian man was killed in one of the air raids, and Israeli soldiers dispersing stone throwers in the Gaza Strip shot dead two teenage boys.
Another Palestinian was killed in a clash with Israeli soldiers in Gaza. The army said the man had been firing at an Israeli convoy.
Since the latest round of Israeli attacks began, Mr Arafat has moved away from his promise to crack down on Palestinian terrorists and close Hamas and Islamic Jihad offices.
"It's impossible for the Palestinian leadership to implement its commitment under the shadow of this comprehensive war," Palestinian Information Minister Yasser Abed Rabbo said.
Security Council discusses crisis
The United Nations Security Council has met in closed session to discuss Israel's decision to cut all ties with Mr Arafat.
Arab nations and the Palestinians had called for an open meeting and a vote on the issue.
The Security Council will resume its discussions later on Friday.
The Vatican has condemned the violence on both sides, and said that there would never be peace in the Middle East until a Palestinian state was created.
The statement from the Roman Catholic church was released after a meeting of bishops from the Middle East.