Tzipi Livni said Israel must react when it is fired upon
The two leading candidates to become Israel's next prime minister have vowed if elected to topple the Palestinian Islamist movement, Hamas, in Gaza.
The threats by Foreign Minister Tzipi Livni and Likud party leader Binyamin Netanyahu came after PM Ehud Olmert warned against making bold statements.
A six-month Egyptian-brokered truce between Israel and Hamas, which runs Gaza, came to an end on Friday.
On Sunday rockets fired by militants in Gaza hit a house in the town of Sderot.
No-one was injured in the attack, though a worker at a nearby farming community was hurt when another device landed in a field.
The Israeli military has said militants fired some 30 rockets and mortar bombs into Israel on Saturday. A Palestinian militant was killed in an Israeli air strike.
At the Israeli cabinet meeting on Sunday, the head of the country's domestic security agency, Shin Bet, said that Hamas had increased the range of its rockets during the ceasefire and could now hit several southern Israeli cities.
Yuval Diskin said the rockets could now reach Kiryat Gat, Ashdod and even Beersheba, about 40km (25 miles) from Gaza.
He also told ministers that while Hamas had renewed its attacks, it was "interested in continuing the truce, but wants to improve its terms".
"It wants us to lift the siege [of Gaza], stop attacks, and extend the truce to include [the West Bank]," Mr Diskin added.
Hamas blamed Israel for the end of the ceasefire on Friday, saying it had not respected its terms, including the lifting of the blockade under which little more than humanitarian aid has been allowed into Gaza.
Israel said it initially began a staged easing of the blockade, but this was halted when Hamas failed to fulfil what Israel says were agreed conditions, including ending all rocket fire and halting weapons smuggling.
Each side accuses the other of breaking the ceasefire
Prime Minister Olmert said during the cabinet meeting that the government had agreed to the ceasefire with Hamas last June with little doubt or hesitation.
"Israel has always hoped for and wanted quiet for the residents of the South and that they should enjoy genuine calm and be free of the threat of unceasing Qassam and mortar attacks that have disrupted life in the South for a very long period," he said.
Mr Olmert and Defence Minister Ehud Barak also warned the cabinet and opposition parties against making "bold statements" about plans for a major military operation in Gaza.
"A government doesn't rush to battle, but doesn't avoid it either," Mr Olmert said. "Israel will know how to give the proper response at the right time in the right way, responsibly."
'Policy of attack'
Shortly afterwards, however, Ms Livni told a meeting of her Kadima party that she would topple Hamas if she became prime minister after the general election on 10 February.
"The state of Israel, and a government under me, will make it a strategic objective to topple the Hamas regime in Gaza," she said. "The means for doing this should be military, economic and diplomatic.
"Israel must react when it is fired upon, must re-establish its force of dissuasion and stop the rockets," she added. "This is what has to be done and this is what I will do."
Mr Netanyahu, whose right-wing Likud party is currently ahead in the polls, meanwhile called for a more "active policy of attack", accusing the current government of being too "passive".
"In the long-term, the toppling of the Hamas regime is inevitable," he said while visiting Sderot on Sunday.
He said residents of southern Israeli towns close to the Gaza Strip were "paying a hefty price for the mistakes made by Livni and her ministers" since the Israeli withdrawal from the territory in 2005.
Ismail Haniyeh, the head of the Hamas government in Gaza and former Palestinian prime minister, dismissed the Israeli threats.
"Nothing can finish off our people," he said. "It is not our people who are escalating the situation; it is the Israeli occupation which should have stuck to the conditions of the truce."
The BBC's Katya Adler in Jerusalem says the countdown to February's election has started with the candidates eager to court an electorate fearful of the future.
UN Secretary General Ban Ki-moon has warned that a "major escalation of violence would have grave consequences for the protection of civilians in Israel and Gaza, the welfare of the Gazan civilian population, and the sustainability of political efforts".