Israeli Prime Minister Ehud Olmert has announced new strikes against the militant Islamist movement Hamas after another deadly missile attack on the Israeli border town of Sderot.
Olmert said during Sunday's cabinet meeting that nobody was immune from Israeli attacks.
"We decide when, how and where we act without accepting any conditions from outside," he said.
Olmert said that Israeli strikes might continue even if rocket fire by Palestinian militants is halted.
On Sunday evening, Israeli forces conducted two airstrikes in the Gaza Strip, hitting a base of the Hamas Executive Force in Dir al-Balah and a rocket-launching position near Beit Lahia. No injuries were reported.
Earlier Sunday, a 36-year-old Israeli Oshri Oz was killed when a missile launched from the Gaza Strip struck his car in the Sderot town centre. Another Israeli civilian was wounded.
The military arm of Hamas took responsibility for the attack. It was the second rocket fatality in less than a week in Sderot, where a woman was skilled on May 21 by a missile launch from Gaza.
The Israeli military said that at least nine Palestinian rockets landed on Sunday in Israel.
A spokesman for Hamas's military wing, the al-Qassam Brigades, later said that it would only agree to a ceasefire after Israel ended its military activities in both the West Bank and Gaza Strip.
"The Hamas movement rejects a free ceasefire deal with the enemy and will continue with the armed resistance until the enemy stops its aggression on our people," said Abu Obeida.
A previous ceasefire since November applied only to Gaza.
A leaflet issued by the al-Aqsa Martyrs' Brigades, affiliated with Palestinian Authority President Mahmoud Abbas' Fatah movement, said that group would only agree to a ceasefire that includes both territories.
Abbas has been trying recently to renew the ceasefire with Israel in a gradual process that would start in the Gaza Strip and then later be extended to the West Bank. He has been critical of the rocket fire but has not managed to bring it to an end.
The Israeli air force attacked other Hamas posts late Saturday in Rafah and the Jabaliya refugee camp, wounding two Palestinians.
Earlier, Israeli airstrikes killed five members of the Hamas police militia in the Gaza Strip. Another 20 Palestinians were wounded in the attacks.
Israeli police had raised alert levels on Saturday night to the highest possible non-emergency level, following a Saturday afternoon shooting on security forces by two Palestinian militants in East Jerusalem, the Israeli online news service Ynet reported on Sunday.
On Saturday afternoon, two armed Palestinians were killed when they opened fire on a police patrol on the West Bank border with East Jerusalem, wounding four officers. A third Palestinian, uninvolved in the attack, was killed in the crossfire.
The Hamas movement had responded to fresh strikes against its forces in the Gaza Strip by saying that renewed attacks in Israel were only a matter of time.