(Adds defence sources, paragraph 1-4)
By Adam Entous
JERUSALEM, Dec 21 (Reuters) - The top candidates to become Israel's next prime minister vowed on Sunday to topple Hamas in the Gaza Strip and officials authorised strikes on a wider range of Islamist targets after a six-month-old truce ended in violence.
The threats by Foreign Minister Tzipi Livni and right-wing Likud party chief Benjamin Netanyahu followed a cabinet meeting in which outgoing Prime Minister Ehud Olmert cautioned against rushing into a large-scale ground operation in the Hamas-ruled enclave in response to escalating rocket fire by militants.
Such an operation could result in heavy casualties on both sides, fuel a major humanitarian crisis in the aid-dependent Gaza Strip and spark an international outcry against Israel.
Until now, the Israeli military has carried out limited air strikes against rocket launchers, but defence sources said the air force now had a green light to go after other Hamas targets as well. The sources would not identify what those potential targets might be and when those air strikes might begin.
If elected premier in a Feb 10 election, Livni, who heads the centrist Kadima party, said her government's "strategic objective" would be to "topple the Hamas regime" using military, economic and diplomatic means. She did not set a timetable.
Netanyahu, Livni's main rival for the premiership, called for a more "active policy of attack", accusing the current government of being too "passive".
"In the long-term, we will have to topple the Hamas regime. In the short-term, ... there are a wide range of possibilities, from doing nothing to doing everything, meaning to conquer Gaza," Netanyahu said during a visit to a house in the southern Israeli town of Sderot that was hit by a rocket.
Palestinian militants have fired nearly 60 of the makeshift rockets and mortar shells at Israel since the Egyptian-brokered ceasefire with Hamas ended on Friday, the Israeli army said. Over the weekend, an Israeli air strike killed one militant and at least one person in Israel was injured by a shell shrapnel.
Ismail Haniyeh, head of Hamas's government in Gaza, brushed aside Israeli threat: "Nothing can finish off our people."
Hamas official Ayman Taha said the Islamist group, which took over the Gaza Strip in June 2007 after routing rival Fatah forces loyal to Palestinian President Mahmoud Abbas, predicted Hamas's rule would outlive Livni's.
Olmert had cautioned his cabinet against making "bold statements" about an operation in the Gaza Strip and suggested that he favoured a wait-and-see approach.
"A government doesn't rush to battle, but doesn't avoid it either," Olmert said. "Israel will know how to give the proper response at the right time in the right way, responsibly."
Underscoring the military challenge facing Israel in the densely-populated Gaza Strip, Defence Minister Ehud Barak said even an incursion involving two-to-three divisions, or more than 20,000 troops, may not be enough to stop rocket fire.
Government ministers promising to topple Hamas "do not know what they are talking about", Barak said.
But pressure on the government to act is mounting.
Yuval Diskin, head of the Shin Bet domestic intelligence agency, told ministers on Sunday that Hamas has longer-range rockets that could strike the city of Beersheva, a major population centre some 40 km (25 miles) from the Gaza Strip.
"It needs to be clear. A strike in Gaza will come, and it will be hard and painful," cabinet minister Isaac Herzog said.
Polls show a tightening race between Livni and Netanyahu to replace Olmert as prime minister, and both candidates have stepped up anti-Hamas sabre-rattling in recent days.
Since the ceasefire ended on Friday, the Islamic Jihad group has claimed responsibility for most of the rocket fire at Israel, which kept border crossings closed, preventing the passage of humanitarian supplies.
The ceasefire had been eroding since early November when a deadly Israeli raid prompted militants to step up rocket attacks, most of which cause no injuries and little damage. (Additional reporting by Ari Rabinovitch in Jerusalem and Nidal al-Mughrabi in Gaza; Editing by Katie Nguyen)