The decision to continue the policy of "targeted killings" was taken during a meeting of military and security leaders at the Defence Ministry in Tel Aviv, Israeli army radio reported on Tuesday.
Mofaz' statements came one day after the assassination of Hamas' spiritual leader Shaikh Ahmad Yasin in Gaza by Israeli fire.
Hamas is considered a "strategic enemy of Israel and should be destroyed," Mofaz said at the meeting.
Meanwhile, Gaza is mourning the loss of Yasin.
"Schools, universities, and shops in Gaza city are closed, as Palestinian citizens mourn the assassinated Hamas leader Shaikh Ahmad," reported Aljazeera correspondent in Gaza, Samir Abu Shamalah.
On Monday, the body of Yasin was carried through the streets of Gaza city by resistance fighters as they made their way to al-Shuhada (Martyrs) cemetery.
Tens of thousands of mourners, some carrying billowing Hamas flags, flooded the streets for the funeral procession, the largest gathering in Gaza city in recent memory.
Mourners jostled to touch Shaikh Yasin's coffin, draped in the green flag of the movement that he founded. Two Israeli helicopters flew overhead and the sky was blackened from the smoke of burning tyres.
The procession left Gaza's al-Shifa hospital, heading first towards Yasin's house in Gaza. A brief funeral service was held at a mosque in the centre of the city.
Many of the mourners from a cross-section of Palestinian factions chanted "vengeance, vengeance" while resistance fighters fired off piercing volleys into the air.
Among the crowds gathered outside Yasin's house were three women brandishing M-16 assault rifles. One of the women, who was in her 60s, said she was prepared to take part in an attack in retaliation.
A man screams as he views the
body of Shaikh Yasin
"We are all fighters, all martyrs. We are all prepared to be martyrs," she told AFP.
At the cemetery, the 67-year-old Yasin's coffin was carried to the grave between two rows each of 200 resistance fighters.
His burial took place just hours after he was killed in an Israeli helicopter missile attack.
Israeli helicopter gunships fired missiles at Yasin as he left a mosque after dawn prayers, killing the Hamas leader .
One witness who lives near the mosque told reporters what happened moments after the first explosion.
"I looked to see where Shaikh Ahmad Yasin was," he said. "He was lying on the ground and his chair was destroyed. People there darted left and right. Then another two missiles landed."
At least nine people died in the attack including at least two of Yasin's bodyguards. Ten more were wounded. Yasin's two sons were slightly injured.
Marked for death
The Israeli army later admitted it had carried out the killings.
At least nine others died in missile
attack on the Hamas leader
Deputy Defence Minister Zeev Boim confirmed the attack on Israel Radio, saying: "I said for a long time that Yasin is a target for killing. He was not immune."
Israel vowed to step up operations to track and kill Palestinian resistance fighters after a string of bombings, including one at a strategic port last week in which 10 people were killed.
Israeli Prime Minister Ariel Sharon personally supervised the attack on Yasin, Israeli public radio reported. Sharon had given the green light to his assassination and supervised the operation, the radio said.
After the attack, Sharon congratulated security forces and said "the war on terror" would continue.
"The state of Israel this morning hit the first and foremost leader of the Palestinian terrorist murderers," Sharon said in his first public reaction to the strike. "I want to make clear the war on terrorism is not over and will continue daily everywhere."
Yasin had been used a wheelchair since an accident as a teenager paralysed him. He was also partially blind.
He was sentenced by Israel in 1989 to a life term for founding Hamas and urging Palestinians to attack Israel.
But Israel released him in 1997 as a goodwill gesture to Jordan's King Husayn after a botched attempt to assassinate Hamas leader Khalid Mishal in Jordan.
Who is next?
The assassination of Shaikh Yasin
has outraged Palestinians
Within hours of the killing, Israeli Foreign Minister Silvan Shalom told the US media that his government had no plans as yet to assassinate the Palestinian president.
Although Yasir Arafat has been a virtual prisoner in Ram Allah for the past 30 months, he has not been attacked by Israeli helicopter gunships.
Asked on CNN television if a plan to assassinate Yasir Arafat was on the cards, Shalom replied: "Not at all."
Israel is only killing "those that caused us hundreds of casualties of innocent Israeli peoples".
Shalom spoke after a meeting at the White House on Monday with US Vice President Richard Cheney.
He was also due to meet on Monday Secretary of State Colin Powell and National Security adviser Condoleezza Rice.