Ephraim Sneh, Israel's deputy defence minister, told public radio: "We feel today free to do things that we avoided doing several months ago."
An Egyptian security delegation, headed by General Bourhan Hamad and which is based permanently in the Gaza Strip, was to meet representatives of all the Palestinian factions on Wednesday in an effort to save the truce.
Islamic Jihad, which has not recognised the November 26 ceasefire with Israel, was also due to take part in the meeting, according to Egyptian and Palestinian officials.
Hamas's military wing fired scores of missiles into Israel on Tuesday, saying the truce "no longer exists".
The Izz al-Din al-Qassam Brigades said it fired 30 rockets and 61 mortars from Gaza.
The Hamas-led Palestinian government called for the truce to be restored.
Israel said at least six rockets were fired, causing minor damage but no injuries as Israel celebrated its Independence Day.
Peretz warned the Palestinian government against allowing more attacks while Mahmoud Abbas, the Palestinian president, urged Israeli restraint.
"The violation of the truce is an exceptional event that will not last," Abbas said in Rome on Tuesday.
"I take this opportunity to appeal to Israel to show the necessary self-control so that this will not happen again."
The Palestinian government, which Abbas's Fatah faction jointly runs with Hamas, called for the ceasefire to remain in place.
"The government is interested to keep the ceasefire and the calm and we are trying, through consultation and discussion with the Palestinian factions, to take a position in order to protect our people," said Ghazi Hamad, government spokesman.
Tuesday's attacks marked the first time that Hamas claimed responsibility for launching rockets into Israel since a November 26 ceasefire took effect between the army and Palestinian fighters.
Abu Obaida, a spokesman for the Brigades, said of the truce: "It's the Israeli enemy that has not respected it, and now it's the turn of Palestinian groups."
Observers say there has been a debate within the Hamas leadership over whether the group has to take a harder line towards Israel, but the group denies any divisions.
Abu Obaida told Al Jazeera: "There is no co-ordination between the military [wings] of the Palestinian resistance faction and the government or the [Palestinian] Authority."
He said the attack was in response to the death of nine Palestinians, two teenagers and five fighters among them, by Israeli troops over the weekend in the occupied West Bank and Gaza.
The deaths marked the bloodiest weekend of Israeli-Palestinian violence since the November truce and sparked calls for retaliation on the part of Palestinian armed groups.
Under the terms of the November ceasefire, the Israeli army withdrew troops from the Gaza Strip and Palestinian fighters there were supposed to halt rocket fire.
Until Tuesday, the truce had largely held despite violations by both sides.