But Mr Mofaz may find it hard to draw Mr Olmert's supporters keenly into his camp.
Livni and Mofaz are vying to succeed Ehud Olmert as Israel's next prime minister.
They say Mofaz's threat is meant to serve primarily as a deterrent to Iran.
Mr. SHAUL MOFAZ (Defense Minister, Israel): (Through Translator) Israel cannot accept an Iran with nuclear capability.
Mr Mofaz and his generals promise a frank investigation into the disastrous Hebron firefight.
But Mr Mofaz has not ruled out military action if diplomacy and sanctions fail.
"Tonight, Kadima has decided to withdraw from the national unity government, " Mofaz told reporters after the meeting.
Egypt said it would work to extract such guarantees, but Shaul Mofaz, Israel's defence minister, ruled them out.
There will be a further army inquiry but, at least at this stage, General Mofaz offered no apology.
ECONOMIST: Israel��s army: A new, perhaps dangerous, freedom | The
Mr Mofaz's Kadima has 28 seats in parliament to the 27 held by Mr Netanyahu's lot, the Likud.
ECONOMIST: Israeli politics: Can Binyamin Netanyahu do a somersault? | The
Speaking at Israel's most high profile strategic conference, Defense Minister Shaul Mofaz warned Iran against pursuing a nuclear weapon.
The harder-line Mr Mofaz, a hawkish former chief of staff of the army, was against an alliance with Meretz.
She emerged with 43% of the vote, just 1% ahead of her main rival, Shaul Mofaz, the transport minister.
One Israeli Cabinet member, Shaul Mofaz, recently said it "will attack" Iran if the nuclear program was not halted.
Mofaz's plan is to recognize and seek to negotiate a settlement with Hamas.
Mr Mofaz has consistently criticised Mr Netanyahu's lack of enthusiasm on this front.
ECONOMIST: Israeli politics: Can Binyamin Netanyahu do a somersault? | The
This follows the lines of Mr Mofaz's initial policy in the West Bank, when he was army chief of staff.
As an Agence France Press (AFP) story noted, Mofaz said such an operation could only be done with U.S. support.
If the early election had gone ahead, Kadima under Mr Mofaz would have suffered badly, according to all the pollsters.
Among those expected to run against Mr Netanyahu are Shaul Mofaz, the defence minister, and Silvan Shalom, the foreign minister.
ECONOMIST: The ��bulldozer�� sends tremors through Israeli politics
Mr. MOFAZ: (Through translator) I want to appeal to the Iranian president, who is from the city where I was born.
Yediot Ahronot on Friday published excerpts of an interview with Mofaz that is to appear in the paper's Sunday holiday edition.
CNN: Israeli politician threatens Iran with attack over nukes
"We want to make sure we're prepared for every option, " Mofaz says.
Shaul Mofaz, a former defence minister, and Moshe Yaalon, a minister and former army chief of staff, cancelled visits rather than risk arrest.
Mofaz was reiterating a prevailing view among Kadima officials and other Israeli politicians that international sanctions targeting Iran and its nuclear program aren't working.
CNN: Israeli politician threatens Iran with attack over nukes
Israel's prime minister, Ariel Sharon, and his new hardline defence minister, Shaul Mofaz, may yet be cautious with their response to the kibbutz atrocity.
Mr Sharon even pointedly omitted Mr Netanyahu from a meeting he held with Mr Mofaz and other security officials to plan the military retaliation.
In 2009 Mr Mofaz proposed the immediate creation of a Palestinian state on some 60% of the West Bank, followed by negotiations over the remainder.
Mr Sharon plainly intends to groom others for that, including the former army chief of staff, Shaul Mofaz, and the mayor of Jerusalem, Ehud Olmert.
On Tuesday, Israeli Defense Minister Shaul Mofaz said the Palestinians would be allowed to vote at post offices, a method they have used in the past.
应用推荐