"From the moment when Hamas continues on the path of terrorism, nobody in the movement will benefit from immunity," Mr Mofaz said when asked on army radio about the possibility of Mr Haniya being subject to a targeted killing operation.
Mr Haniya has been given the task by Palestinian leader Mahmoud Abbas of forming a government following the group's election victory in January.
Hamas has carried out dozens of anti-Israeli suicide attacks during the course of a five-year Palestinian uprising, although none in the past 12 months.
Killings to continue
Two Hamas leaders, Sheikh Ahmed Yassin and Abdelaziz al-Rantissi, were killed in Israeli air strikes two years ago. Mr Haniya was also present with Mr Yassin during an earlier assassination attempt in September 2003.
More recently, Israel has targeted leaders of the extremist Islamic Jiahd movement which has continued to carry out attacks, including seven suicide bombings in the past year.
Two members of Jihad died in an air strike on Gaza City on Monday but three children were also killed in the attack, prompting criticism from the United Nations.
But Mr Mofaz vowed that the so-called targeted killing operations would continue.
"This policy is just and it will be pursued," he said, adding that the strikes were carried out with "surgical precision".
Questioned about the deaths of an eight-year-old and two teenage boys in Monday's strike, Mr Mofaz said he was "sorry when civilians are hit."
The UN Middle East peace envoy, Alvaro de Soto, stressed his opposition to what he called "extra-judicial killings”, which posed a danger to innocent bystanders.
"While recognising Israel's right to defend itself, particularly from rocket attacks, I call on the Israeli military authorities to desist from extra-judicial killings and show maximum restraint at this delicate time."
Israeli elections
Mr Mofaz's comments come less than three weeks before Israel’s general election on March 28, with the ruling Kadima party keen to deflect any suggestion they are "soft on terrorism."
Benjamin Netanyahu, leader of the right-wing opposition Likud party, has claimed Hamas's victory was a direct result of the government's decision to pull troops and settlers out of the Gaza Strip last year.
Israel’s hardline candidates have accused Acting Prime Minister and Kadima party leader Ehud Olmert of being too soft on Hamas, which is sworn to Israel's destruction and refuses to renounce violence.
Another leading Kadima candidate, the former Shin Beth internal security chief Avi Dichter, also threatened Mr Haniya over the weekend.
"If Haniya and his people continue their policy of terror and assassinations when they are in power, they will find themselves behind bars or joining Sheikh Yassin," he said.
Hamas reacted to Mr Mofaz's comments by accusing Israel of conducting "state terrorism".
"Hamas does not fear these threats and blackmail. We are committed to the defence of our rights and our people whatever the price," spokesman Sami Abu Zuhri told AFP.
"These comments by the Israeli defence minister are an illustration of state terrorism."