Israeli Prime Minister Ariel Sharon has warned that there will be no peace deal with the Palestinians unless they fight "terror".
Three militants launched the first attack early on Sunday
Mr Sharon was addressing a meeting of his own Likud Party hours after five Israelis and five Palestinians died in the first major clashes since last week's US-led peace summit in Jordan.
Speaking over loud boos and jeers from Likud hardliners opposed to the peace plan, known as the roadmap, Mr Sharon said Israel had to make concessions to achieve peace with the Palestinians.
In a message likely to infuriate Palestinians he said Israel would never allow Palestinian refugees to return to their former homes in Israel.
He said his government would implement the roadmap "in stages and with open eyes", but he said the Palestinians "must dismantle the terror organizations" first.
Palestinian militants have boycotted ceasefire talks their Prime Minister Mahmoud Abbas - also known as Abu Mazen - over his failure to address the refugee issue as well as that of Jerusalem - claimed by both sides as their undivided capital.
Three militant groups have said they carried out one of the attacks on Sunday when three Palestinian gunmen attacked the Erez army checkpoint between the Gaza Strip and Israel, killing four Israeli soldiers and wounding four others before themselves being shot dead.
Later in the day, another Israeli was killed along with two Palestinian gunmen in the West Bank city of Hebron, the Israeli army said.
US Secretary of State Colin Powell urged both sides not to allow the latest violence to derail the search for peace.
The attacks are being seen as a serious blow to the Palestinian prime minister who pledged at the summit to crack down on militants.
Help for Palestinians
"What we have to do now is make sure we don't allow this tragic, terrible incident to derail the momentum of the roadmap that got started... last week," Mr Powell said.
The US reaction was measured, says the BBC's Steven Kingstone in Washington.
In the past, the US has blamed Palestinian leader Yasser Arafat and reasserted Israel's right to self-defence, our correspondent adds.
ROADMAP MAIN POINTS
Phase 1 (to May 2003): End to Palestinian violence; Palestinian political reform; Israeli withdrawal and freeze on settlement expansion; Palestinian elections
Phase 2: (June-Dec 2003) Creation of an independent Palestinian state; international conference and international monitoring of compliance with roadmap
Phase 3 (2004-2005): Second international conference; permanent status agreement and end of conflict; agreement on final borders, Jerusalem, refugees and settlements; Arab states to agree to peace deals with Israel
The softer tone reflects American confidence in Abu Mazen who - unlike Yasser Arafat - is regarded by Washington as someone to do business with, he says.
Mr Powell said the United States would give Abu Mazen practical help to deal with the militant groups.
A BBC correspondent in Jerusalem, Richard Galpin, says the Gaza attack - claimed by Hamas, the Islamic Jihad, and the Al-Aqsa Brigades - leaves the new Palestinian prime minister in "an extremely difficult position".
Israeli Government spokesman Avi Pazner said if Mr Abbas "does not fight the terrorists, we will".
Following the attack Abu Mazen postponed a planned trip to Gaza aimed at pushing for a ceasefire.
One of the groups claiming responsibility for the attacks, the al-Aqsa Brigades, is linked to Yasser Arafat's Fatah movement, of which Abu Mazen is himself a long-standing member.