"I have given instructions to intensify the strength of action by the army and security services, to hunt down these terrorists, those who send them ... and those who harbour them," Ehud Olmert said at a cabinet meeting on Sunday.
Israel sent troops and tanks into the south of the territory on Wednesday after Palestinian gunmen seized Corporal Gilad Shalit in a cross-border raid last Sunday. It has threatened to begin military operations in the north of Gaza to target Palestinians who have been firing rockets into Israel.
The group holding Shalit has offered to give Israel information about him in exchange for the release of hundreds of prisoners, a deal Israel has rejected.
"These are difficult days for Israel, but we have no intention of giving in to any form of blackmailing," Olmert said on Sunday. "Everyone understands that giving in to terror today means an invitation to the next act of terrorism, and we will not act that way."
Olmert addressed his cabinet after an air strike on the empty offices of Ismail Haniya, the Palestinian prime minister.
Kofi Annan, the United Nations secretary general, called the attack "inadvisable."
"I remain very concerned about the need to preserve Palestinian institutions and infrastructure," Annan said. "They will be the basis for an eventual two-state solution and are thus in the interests of both Israel and the Palestinians. It would therefore seem inadvisable to carry out actions that will have the opposite effect."
Israeli security forces have said the operation in Gaza could last months. "We have to take a deep breath ... There is no magic solution," said Yuval Diskin, head of the Shin Bet.
Israeli security forces said the
offensive could last months
A negotiated end to the crisis appears increasingly unlikely. Palestinian officials said Egyptian-led diplomatic efforts to free Shalit were continuing but making little progress because of Israel's offensive. "I'm not hopeful," senior Abbas aide Saeb Erekat said.
Major General Amos Yadlin, the Israeli army's chief of intelligence, said the mediation efforts were stymied because no one knows whom to talk to about Shalit.
"The Egyptians are trying to mediate, but most of the negotiations they are doing with themselves," he told the Israeli cabinet, according to a participant in the meeting.
Hamas's armed wing responded to the missile strike on Haniya's office by threatening to attack Israeli power plants, institutions and schools if more air strikes were carried out against Palestinian infrastructure.