"The current situation is unacceptable and cannot be allowed to continue," Sharon said at the start of the weekly cabinet meeting on Sunday.
"The Tsahal (army) and the security forces have received orders to operate without any limits on time or their modus operandi to act against the terrorist organisations.
In the first Palestinian reaction to Sharon's new policy, Palestinian foreign minister Nabil Shaath said the new military campaign under way in Gaza will only serve to further undermine the peace process,.
"This policy will not serve the peace process and I ask the Israeli people to reject this Sharon policy," Shaath said after a meeting with his Japanese counterpart Nobutaka Machimura in Ram Allah.
A Sharon spokesman on Friday said the Israeli prime minister would refuse to meet with Palestinian president-elect, Mahmud Abbas, until he acted against armed resistance groups behind Thursday night's attack at the al-Mintar (Karni) crossing.
At least six Israelis and three Palestinians were killed in the explosion set off by Palestinian resistance fighters there.
"This policy will not serve the peace process and I ask the Israeli people to reject this Sharon policy"
Palestinian Foreign Minister
Fifteen people were also injured in the attack, the biggest since Abbas won the election to succeed Yasir Arafat as head of the Palestinian Authority.
Shortly before Sharon's statements, an Israeli drone bombed a Palestinian home in the al-Salatin district west of Bait Lahya in the northern Gaza Strip.
The home was severely damaged, but none of its residents, a 16-member-family, were reported to have been injured.
An Israeli military spokesman said the attack targeted a workshop used for making rockets and mortar shells.
Meanwhile, Hamas' military wing, Izz al-Din al-Qassam Brigades, has issued a statement claiming responsibility for firing two Qassam rockets at the Jewish town of Sderot inside in the northern Gaza Strip.
Abbas wants a halt to Qassam
rocket attacks on Israeli targets
In a separate statement, the movement claimed responsibility for firing another two Qassam rockets at the Eli Sinai settlement in northern Gaza Strip.
An Israeli spokesperson said no injuries were sustained due to the rocket attacks.
Newly elected Palestinian President Abbas had called for an end to Qassam rocket attacks on Israeli targets, but he has largely been ignored by Palestinian resistance groups.