Israel and Hamas, the Palestinian group, declared separate ceasefires last month after a 22-day Israeli offensive in the Gaza Strip that killed at least 1,300 Palestinians, many of them women and children.
Thirteen Israelis were also killed, three of them civilians, by Palestinian rockets and mortars.
Halting the Palestinian fire was one of Israel's stated aims for the air, naval and ground assault that also caused hundreds of casualties and destroyed much of the territory's infrastructure.
But there has been sporadic rocket fire across the border and a number of Israeli air raids since the truces were announced.
"This is an attempt to find a false excuse to escalate the aggression against the Palestinians"
Olmert said at the cabinet meeting: "The situation ... in recent days has increased in a manner that does not allow Israel not to retaliate in order to make sure that our position ... is understood by those involved in the fire.
"The response will come at the time, the place and the manner that we choose."
Two candidates to replace Olmert after parliamentary elections on February 10 also used the cabinet meeting to threaten further action against Hamas.
"Hamas was given a very serious blow and if necessary it will be given another blow," Ehud Barak, Israel's defence minister and the leader of the Labor party, said.
Tzipi Livni, the foreign minister and head of Olmert's Kadima party, said that Israel must respond to rocket attacks "immediately".
"We mustn't sign arrangements with Hamas, but rather use force against this organisation," she said.
"Israel will respond whether the Qassam [rocket] causes injuries or not, and this is how I will act as prime minister as well. We must use force and a lot of force."
Al Jazeera's Jonah Hull, reporting from Jerusalem, said that the cabinet wanted to show that offensive had been successful in undermining Hamas's ability to operate in Gaza, but the continuing rocket fire brought that into question.
"For Barak and Livni there is a strong desire to show the Israeli public that the security interest of Israeli citizens is still uppermost in their minds," he said.
"The Israeli government is keen to demonstrate, as much for domestic consumption as anything else with an election coming up, that it is firmly committed to hitting Hamas hard in reponse to any firing of rockets."
Hamas said that the statements were a "campaign stunt" in the run-up to the February 10 elections.
"We condemn the statements by Olmert and others today threatening the Gaza Strip," Taher al-Nunu, a Hamas spokesman, said in a statement on Sunday.
"This is an attempt to find a false excuse to escalate the aggression against the Palestinians, to destroy the Egyptian efforts to improve the calm and to use pressure against the Palestinian people to accept Israeli conditions in those talks."
Egyptian mediators have been attempting to secure a long-term ceasefire addressing Israel's concerns over rocket attacks and weapons smuggling into Gaza, as well Palestinian demands for the siege of the territory to be lifted.
Benjamin Netanyahu, the leader of the Likud party which is currently the frontrunner for the election according to opinion polls, saved his rhetoric for Iran, saying that if elected prime minister his first task would be to tackle its nuclear threat.
|Opinion polls suggest Netanyahu is frontrunner to be Israel's next prime minister [EPA]
"Iran will not be armed with a nuclear weapon. That is a fact," he said on Israel's Channel 2 television.
Netanyahu said that he would do "everything that is necessary to make this statement come true".
The United States and allies have said that Iran is enriching uranium for use in nuclear weapons, but Tehran insists that its nuclear programme is for civilian enery production.
Al Jazeera's Hull said that Netanyahu was the only one of the contenders for the premiership who was not involved in the planning and execution of the war on Gaza, yet it actually served to boost his poll ratings.
"Netanyahu has insisted that the war was not a success, that it should have gone on longer, that it should have been harder and had the effect of collapsing or destroying Hamas altogether," he said.
"But Netanyahu also goes one step further in his platform of total security for Israel, bringing in Iran ... Netanyahu knows that stance, Iran very firmly linked in the minds of Israelis to Hamas, is a very popular one."