The three-week offensive was launched with the twin aims of retrieving a corporal abducted by Hamas militants and stopping rocket fire.
Tanks and troops in the northern town of Beit Hanun conducted what is their deepest Gaza incursion since withdrawing from the territory barely 10 months ago.
Called "Operation Summer Rain" the offensive has left at least 87 Palestinians and one Israeli soldier dead since July 5.
Israel opened up a second front after Hezbollah captured another two soldiers last week and has pounded Lebanon with air strikes for six days killing more than 200 people and seeing world leaders scramble to head off all-out war.
Addressing MPs in the Israeli parliament, Mr Olmert vowed no let-up in Israel's deadly offensives against either Hamas or Hezbollah.
"We will fight the Palestinians without fail until terrorism stops, until
Corporal Gilad Shalit is returned safe and sound, and Qassam rocket fire ceases," he said.
"We will not cease our operations. In both cases, in Lebanon and in the Gaza Strip, this is an act of self-defence, because the nation is at a moment of truth," Mr Olmert said.
Ministry collapses
Overnight fighter jets bombed the foreign ministry in Gaza for the second time in a week.
An F-16 jet dropped a missile on the building, which had already been badly damaged in a raid Thursday.
The five-storey building collapsed causing extensive damage to the nearby planning and finance ministries.
Three residents of nearby houses were also wounded, medical and security sources said.
Israel has already bombed the Gaza offices of Haniya and those of his interior minister Siad Siam this month.
In response Palestinians fired eight rockets into southern Israel.
Israel justified the air strikes by accusing foreign minister Mahmud al-Zahar, a leading member of Hamas, whose armed wing was jointly responsible for Corporal Shalit's abduction, of planning "terrorist attacks".
Palestinian Prime Minister Ismail Haniya said Israeli attacks on ministries "prove these actions are to paralyse the work of the Palestinian government and to destroy the foundations of the Palestinian political system".
West Bank
Ground troops have also rounded up a third of the Hamas cabinet in the occupied West Bank, although one of the ministers has since been released.
A 20-year-old resident was killed and a Palestinian gunman left seriously wounded when an Israeli tank opened fire in Beit Hanun, a medical source said.
A second Palestinian, also a young man, was killed by Israeli fire in another incident in Beit Hanun, a local medical source said, while a third was critically wounded in cross-fire between Israelis and Palestinian fighters.
Mr Haniya likened Israel's incursion in Beit Hanun "to what is happening in Beirut, and in all the villages, towns and refugee camps in Lebanon".
However Israeli tanks parked in the middle of the town moved out on Monday evening, Palestinian security sources said.
Witnesses said infrastructure, orchards, the electricity network, water and sewage systems have been damaged in the incursion.
Aid groups have expressed concern about the difficulties of providing assistance to 1.4 million people living in Gaza following months of financial crisis and the suspension of direct Western aid to the Hamas-led government.
Corporal Shalit's capture sparked the worst Israeli-Palestinian crisis since the Hamas-led government was elected in January polls and some of the deadliest fighting in the Palestinian territories for years.