'Severe and disproportionate'
At least 10 rockets and mortar shells were fired into southern Israel from the Gaza Strip on Sunday before Olmert gave his warning.
"We've said that if there is rocket fire against the south of the country, there will be a severe and disproportionate Israeli response to the fire on the citizens of Israel and its security forces," Olmert said on Sunday at a weekly cabinet meeting.
The al-Aqsa Martyrs Brigades, the military wing of the Fatah faction led by Mahmoud Abbas, the Palestinian president, told Al Jazeera that it carried out the attacks.
The Hamas faction seized control of the Gaza Strip from Fatah forces in June 2007, but several other Palestinian groups, including the al-Aqsa Martyrs Brigades, continue to operate in Gaza.
Israel, however, holds Hamas responsible for all rocket fire coming from Gaza.
Halting the Palestinian fire was one of Israel's stated aims for the air, naval and ground assault that killed more than 1,300 Palestinians.
But there has been sporadic rocket fire across the border and a number of Israeli air raids since the ceasefires were announced.
Egyptian mediators have been attempting to secure a longer-term ceasefire addressing Israel's concerns over rocket attacks and weapons smuggling into Gaza, as well as Palestinian demands for the Israeli siege of the territory to be lifted.