Israel's security cabinet has approved plans to step up operations against Palestinian militants in Gaza.
Israeli troops have regularly moved against militants firing rockets
The cabinet said efforts would focus on Hamas and the Islamic Jihad militant group responsible for ongoing rocket attacks against southern Israel.
Authorisation was given for operations to dismantle "terrorist infrastructure" but not for a ground incursion.
Israel has launched a series of air raids following recent rocket strikes, killing more than 20 Palestinians.
At least three people were killed in the latest round of air strikes, aimed against suspected militants and weapons factories in Gaza.
The Israeli decision came as a truce on the streets of Gaza between Palestinian rivals Fatah and Hamas appeared to hold.
Gaza militants have fired more than 50 rockets into Israel over the past week, wounding seven civilians and forcing hundreds to flee. Warning sirens have been wailing several times a day in the town of Sderot.
"If the measured steps we are taking, in the political and military sphere, do not bring about the desired calm, we will be forced to intensify our response," Mr Olmert said at the cabinet meeting.
More than 20 people have died in Israeli air strikes on Gaza in the last five days, which were resumed after a six month lull.
"Hamas people are paying, and will pay, a very heavy personal price for these attacks on the residents of Sderot and nearby communities," Mr Olmert said.
In Gaza City three people, at least two of them Hamas fighters, died when their car was struck, Israeli army officials said.
At least two Hamas militants died when a missile struck their car
The Israeli military said the large size of the explosion indicated the car had been carrying weapons.
Palestinian medical officials said four people were killed in the raids, three of them civilians.
Missiles also destroyed two buildings elsewhere in Gaza, which Israel said were being used as bomb workshops.
There were no reports of injuries in those attacks.
Israel pulled troops and settlers out of the Gaza Strip in 2005 after a 38-year occupation.
Meanwhile, Hamas and rival Palestinian militia group Fatah appeared to be observing another ceasefire in an effort to curb bloody factional infighting in Gaza.
The truce which came into effect on Saturday afternoon is the fifth such pact since violence broke out last Sunday. Since then about 50 people have died in clashes between the two groups.
A Hamas spokesman, Fawzi Barhoum, told the Associated Press news agency he expected the Israeli action to strengthen the latest ceasefire between Hamas and Fatah.
"No-one would accept to fight one another while the Israelis are shelling Gaza," he said.
Gunmen climbed down from rooftop positions and dismantled roadblocks as the ceasefire began to take effect on Saturday.
Relieved residents who had been barricaded for days amid the street fighting took the opportunity to stock up on groceries and other necessities.