Israel attacked Islamist fighters in Gaza on Wednesday for the first time since Hamas seized the territory, and ended an embargo of the Palestinian Authority by opening contacts with a new government in the occupied West Bank.
Israeli soldiers killed four Palestinian fighters in a pre-dawn incursion into the Gaza Strip to hunt for wanted militants. Israel also carried out air strikes against rocket launch sites after one rocket fired from Gaza struck Israel.
Hamas Islamist militias overran President Mahmoud Abbas's Fatah faction and seized control of the territory a week ago.
Two other Palestinian guerrillas, one from Islamic Jihad and another from Fatah were killed in a gun battle in the West Bank, the larger of the two Palestinian territories where Israel maintains an occupying force and Fatah remains dominant.
Foreign Minister Tzipi Livni made Israel's first high-level diplomatic contact with the emergency cabinet formed by Abbas in the West Bank after last week's fighting.
Livni told Palestinian Prime Minister Salam Fayyad in a telephone conversation that the establishment of his emergency government, replacing one headed by Hamas, would allow "progress on various issues ... as well as advance the political process".
Israeli Foreign Ministry spokesman Mark Regev said the exchange "represents the beginning of a dialogue between the two governments, a dialogue that was put unfortunately on hold for the period under which Hamas controlled the Palestinian government".
"We look forward to continuing to engage with the new Palestinian government," Regev said.
Israel had had no contact with the previous Palestinian government for 15 months while Hamas was in power on the back of a parliamentary election win 18 months ago. But it has maintained contacts with Abbas, who was elected separately.
Abbas disbanded the Hamas-led government last Thursday. Hamas has rejected Abbas's new government and still regards itself as head of a unity coalition.
Efforts to bolster Abbas
The result has been a schism that leaves Gaza, a 40-km strip of Mediterranean coast, isolated behind a dense Israeli military cordon and tightening economic blockade.
US President George W Bush and Israeli Prime Minister Ehud Barak pledged at the White House on Tuesday to bolster Abbas, while Israel sought to tighten the screws on Hamas in Gaza.
Bush and Olmert reaffirmed their commitment to the vision of a Palestinian state but offered no concrete plan to achieve a negotiated deal with Abbas.
"He is the president of all the Palestinians," Bush said of Abbas, with Olmert at his side in the Oval Office. "He has spoken out for moderation. He is a voice that is a reasonable voice amongst the extremists in your neighbourhood."
The US and EU pledged on Monday to lift an economic and diplomatic embargo imposed on the Palestinian Authority in March 2006 when Hamas rose to power and refused to drop its refusal to recognise Israel.
As an initial gesture, Olmert has promised to release Palestinian tax revenues withheld since Hamas came to power. He said after the White House talks he would ask his cabinet at its next meeting on Sunday to approve the release of the funds.
The Israeli leader said he wanted to make "every possible effort" to cooperate with Abbas, but he stopped short of bowing to the Palestinian president's push for full-scale peace talks, and Bush showed no sign of pressuring him to do so.