Israel warned Hamas on Tuesday that none of its leaders were safe from attack after a rocket fired by its militants killed an Israeli woman, as Palestinian president Mahmud Abbas arrived in Gaza for talks on shoring up a truce between rival factions.
Abbas was due to meet prime minister Ismail Haniya later to discuss way of strengthening a three-day-old ceasefire that halted deadly clashes between the president's secular Fatah and the premier's Islamist Hamas movements, officials said.
The internecine bloodshed killed more than 50 people, shook the Palestinians' fragile unity cabinet and drove impoverished Gaza, one of the world's most densely populated places, to the brink of civil war.
Coupled with resumed deadly Israeli air strikes, it has also threatened to torpedo international efforts to revive the moribund peace process.
In a new air raid on Gaza, Israel struck an abandoned building of Hamas's paramilitary force, lightly wounding nine people, after issuing a second warning to Hamas leaders in as many days.
"There is no one who is in the circle of commanders and leaders in Hamas who is immune from a strike," Deputy Defence Minister Ephraim Sneh told public radio.
"The political branch of Hamas gives its green light to those who fire rockets," he said. "When someone preaches that the state of Israel should be destroyed, he is not in the political echelon, he is a terrorist in a suit."
The comments came after 35-year-old Shirel Feldman died after a rocket crashed into her car in Sderot late Monday in the first deadly rocket strike inside Israel in six months. It was claimed by Hamas's armed wing.
Israel has pounded Hamas targets in Gaza for nearly a week in response to a sharp increase of rocket fire from the lawless territory. The raids have so far killed 11 civilians and 25 militants.
In the latest international call for restraint from both sides, visiting EU foreign policy chief Javier Solana said: "The violence must stop in all theatres.
"We need a political dialogue to solve the crisis... This is the only solution," Solana said after talks with Israeli Defence Amir Peretz.
The air strikes that Israel resumed after a six-month truce have failed to halt the rocket fire, with three more striking inside the Jewish state on Tuesday without causing any casualties, the army said.
In Sderot, where cars and property charred by rocket hits are a common sight, anger mounted over the state's inability to stop the fire.
More than 120 rockets have hit Israel over the past week, killing one person, wounding 16 and sending hundreds fleeing.
"For a week we've been besieged incessantly by the rockets, non-stop," Alexander Rieman, a 45-year-old teacher, told AFP. "You never know whether your home will be hit, or you, or a friend or a loved one."
Prime Minister Ehud Olmert paid his second visit in a week to Sderot late Monday hours after the deadly rocket strike, pledging support but warning there was "no immediate solution" to the rocket fire.
"I understand the anger, the frustration and the distress and therefore I came to speak with you... to show you that you are not alone and the government is working to alleviate your distress."
But his words fell on deaf ears of the exhausted residents who often describe their life as a Russian roulette.
"Olmert visits accomplish nothing, we've been bombarded for seven years," city official Shalom Halevy told AFP. "We want action -- Hamas leaders have to be eliminated one after the other."
After the security cabinet gave the army the green light on Sunday to ramp up operations, Public Security Minister Avi Dichter said Israel will kill exiled Hamas political supremo Khaled Meshaal "at the first opportunity" and warned the Hamas prime minister Hamas could also be targeted.
Meshaal, who is based in Damascus and already survived an Israeli assassination attempt in Jordan in 1997, held talks with Syrian Foreign Minister Walid Muallem Tuesday, Syria's official SANA news agency reported.
He stressed the "importance of maintaining unity in Palestinian ranks" following the truce between Hamas and Fatah.