At the end of a security discussion, Olmert warned that a large-scale offensive may take place, but so far no decision was made on any operative steps.
A security discussion was held at the Prime Minister's Office for three hours on Wednesday, following a rocket attack on the western Negev and an attempt to kidnap a soldier on Independence Day.
Officials at the Prime Minister's Office said following the meeting, "Due to the sequence of events, Israel will not hesitate to take harsh steps against those attempting to harm its sovereignty by firing missiles at our territory, by attempting to hurt soldiers and through other means."
The prime minister praised the IDF and the Southern Command's activities in thwarting the planned abduction.
In order to improve the army's preparedness, instructions and orders were given for a continued deployment on the Gaza vicinity area in an attempt to thwart additional attacks.
"Israel views the terror activities carried out by Hamas in recent weeks with great severity. After a short period in which it seemed that the ceasefire in Gaza was being partially implemented, the Hamas movement decided to violate it," a statement issued by the Prime Minister's Office said.
"This violation began with a shooting incident against an Israel Electric employee near the Karni crossing a number of weeks ago, and continued with a series of attempted attacks against Israeli targets and using high-trajectory weapons, up to yesterday's incidents.
"Israel did not need any proof that Hamas is a terror organization which did not abandon terror and operated in accordance among the international community since the establishment of the Hamas-led government. Hamas is seeking both to engage in terror and to reap the results of sitting in the unity government. This contradiction cannot be accepted," the statement continued.
'Rockets fired in response to Israel's crimes'
The IDF has been preparing for the possibility of a large-scale operation in the Gaza Strip for months now. Such an operation entails staying in the Palestinian territory for a long time, while risking local civilians who are not involved in terror. Past experience shows that it does not necessarily guarantee significant accomplishments in the short term.
The rockets fired on Independence Day landed in the Ashkelon area and in Gaza vicinity communities. The IDF fired back at the southern Strip.
The Izz al-Din al-Qassam Brigades, Hamas' military wing, claimed responsibility for the attack and said that the rockets were fired "in response to Israel's crimes in the West Bank."
Organization members declared that they had launched 28 Qassam rockets and 61 mortar shells at Israel.
Later is was cleared for publication that the attack was aimed at kidnapping soldiers in order to improve the Palestinians' bargaining abilities in the negotiations for the release of kidnapped soldier Gilad Shalit.