A Palestinian is carried away from the shelling
Among three dead at the Jenin refugee camp is the local leader of the Al-Aqsa Brigades, a radical offshoot of Palestinian leader Yasser Arafat's Fatah faction.
The clashes follow a decision by Israel's security cabinet late on Sunday to step up military operations against the Palestinians, after a series of militant attacks that left more than 20 Israelis dead in less than 24 hours.
An official statement said Israel's security cabinet had approved a broad programme of actions "to put constant military pressure on the Palestinian Authority and terrorist organisations which aims to put the brakes on terror".
EU foreign policy chief Javier Solana, who is to visit Washington on Monday for talks with the US administration on the Middle East situation, has said it is important Mr Arafat be allowed to leave the town of Ramallah, where he has been hemmed in by Israeli forces, to help negotiations.
Out of control
Events have been unfolding at alarming speed, with the gunning down of 10 Israeli troops and settlers in the West Bank on Sunday morning and a devastating suicide bomb attack targeting ultra-Orthodox Jewish families in Jerusalem on Saturday night.
The gun attack on a checkpoint near the Jewish settlement of Ofra in the Ramallah area by a lone Palestinian sniper came just hours after nine Israelis died when a Palestinian suicide bomber blew himself up in the ultra-Orthodox west Jerusalem neighbourhood of Beit Israel.
Israel retaliated by sending F-16 jets to bomb Palestinian targets in the West Bank, killing at least four Palestinian policemen.
Israeli officials said the security cabinet decision would mean an increase in air strikes and raids like those on Jenin and another refugee camp last week.
But a BBC correspondent in Jerusalem says many Israelis are questioning whether Prime Minister Ariel Sharon's strong-arm tactics are curbing Palestinian attacks, or actually generating more of them.
Seventeen months of violence since the Palestinians began an uprising against Israeli occupation of the West Bank and Gaza have claimed the lives of more than 1,200 people - about 900 of them Palestinian and 300 Israeli.
Refugee camps
The al-Aqsa Brigades, an armed offshoot of Mr Arafat's Fatah movement, has claimed responsibility for the suicide bombing.
It also carried out an attack at another checkpoint in southern Israel near the Gaza Strip on Sunday, in which one Israeli soldier died and several others were injured.
The latest upsurge in violence follows Israel's unprecedented assaults on the Jenin and Balata refugee camps which left more than 20 Palestinians dead.