"We'll keep striking them," said Olmert. "God willing, we won't harm any innocent civilians, but we won't hesitate harming those involved in terror."
Olmert intends to make a "heartfelt" approach to the residents of Gaza in the next few days, urging them to understand they are the real victims of the terror emerging from the strip.
"There is no magic cure for this problem," said Olmert. "I know everyone wants me to say we have the answer, some button we can push to make everything okay.
"There is no timetable we have to follow, no outside limitations" said Olmert.
"We will decide when, where, how and if we take action. It will not be dictated from outside", he added.
Any agreement between Hamas and Fatah in Gaza is their own affair," stressed Olmert.
"Whether or not Hamas opens or ceases fire, I can't promise we'll go along with their decision," he added.
"We have nothing to do with any internal agreement they might reach and we have to prepare for the long run," said Olmert.