The raids came days after a truce with Hamas expired.
Israeli Defence Minister Ehud Barak said "there is a time for calm and a time for fighting, and now the time has come to fight".
But the exiled leader of Hamas, Khaled Meshaal, called for a new intifada, or uprising, against Israel, in response to the attacks.
The movement's Gaza leader, Ismail Haniyeh, said there would be no white flags and no surrender. "Palestine has never witnessed an uglier massacre," he said.
Israel hit targets across Gaza, striking in the territory's main population centres, including Gaza City in the north and the southern towns of Khan Younis and Rafah.
Mr Olmert said "we tried to avoid, and I think quite successfully, to hit any uninvolved people - we attacked only targets that are part of the Hamas organisations".
And that fucking cunt Livni Shtipi can SUCK MY COCK!! And keep Sucking it.