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.
Tzipi Livni, the Israeli foreign minister and a candidate for prime minister in parliamentary elections on February 10, has also threatened to hit back at any rocket fire with military action.
“Israel will keep hitting Hamas. We did it in operation “Cast Lead” and we will continue doing so. I do not intend to reach any agreements with Hamas,” the Kadima party leader told Israel’s Channel 2 TV in an interview.
“Agreements I make with people who accept my existence. They [Hamas] do not recognise Israel and they do not renounce violence and terrorism.
“They will not be a party to an agreement and therefore the people of Gaza have to expel Hamas from within them.”
She delivered her remarks as she answered questions posted on Youtube, the video-sharing website.
Ehud Barak, the defence minister and Labor party chief, and Benjamin Netanyahu, leader of the Likud party, who are battling for the premiership, also took part in the programme.
Barak said: “We never relate military operations to politics.
“But it is clear it was an opportunity for the Israeli public to look at the realities of Israel and realise once again that, unlike reality TV shows, these are real life which needs real leadership and not screen leadership.”
Netanyahu, currently the frontrunner 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.
“Iran will not be armed with a nuclear weapon. That is a fact,” he said.
Netanyahiu 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.