Lieberman also said his party was quitting Prime Minister Benjamin Netanyahu’s coalition, leaving the premier with only a one-seat majority in parliament.
Elections are not due until November 2019, but Lieberman’s resignation increases the likelihood of an earlier vote.
“What happened yesterday — the truce combined with the process with Hamas — is capitulating to terror,” Lieberman told journalists in explaining his reasons for resigning.
“What we’re doing now as a state is buying short-term quiet, with the price being severe long-term damage to national security.”
He added later: “We should agree on a date for elections as early as possible.”
Netanyahu has defended Tuesday’s ceasefire deal that ended the worst escalation between Israel and Palestinian fighters in Gaza since a 2014 war.
An official from Netanyahu’s Likud party hit back at speculation that early elections would be called and said the prime minister would take charge of Lieberman’s portfolio at least temporarily.
“There’s no obligation to go to an election in this time of security sensitivity,” the official said on condition of anonymity.
A Likud spokesman said later in the day that Netanyahu had begun consultations with heads of parties in his coalition to stabilise it.
The party of far-right Education Minister Naftali Bennett, a Netanyahu rival, was threatening to withdraw from the coalition if he was not given the defence portfolio.
Lieberman, a security hardliner, heads the right-wing Yisrael Beitenu party, which holds five seats in the 120-seat parliament, the Knesset.
Before taking over as defence minister, he said he would give Hamas leader Ismail Haniya 48 hours to hand over two detained Israeli civilians and the bodies of soldiers killed in the 2014 war “or you’re dead”. He later backed off and said he was committed to “responsible, reasonable policy”. The ceasefire held yesterday, but Netanyahu was seeking to combat criticism of the decision.
Beyond Lieberman’s resignation, several hundred Israelis living near the border with Gaza protested on Tuesday night to call for further action against its rulers Hamas.
Netanyahu defended his strategy and said: “Our enemies begged for a ceasefire.
“In times of emergency, when making decisions crucial to security, the public can’t always be privy to the considerations that must be hidden from the enemy,” he said at a ceremony yesterday.
Hamas portrayed the ceasefire as a victory and thousands of residents of the blockaded enclave took to the streets late Tuesday to celebrate.
Yesterday, Gazan demonstrators burned pictures of Lieberman and sweets were handed out in the streets, while Hamas called his resignation a “victory.”
The Egyptian-brokered truce was announced by Gaza fighter groups, including Hamas, on Tuesday.
A diplomatic source familiar with the agreement said it involved returning to arrangements put in place following the 2014 war, but warned: “The situation remains very precarious and can blow up again.
“What we have seen in the past 48 hours was very dangerous and no efforts should be spared to avoid similar flare-ups.”
The violence saw seven Gazans killed in 24 hours as Israeli strikes targeted fighters and flattened buildings, sending fireballs and plumes of smoke into the sky.
Sirens wailed in southern Israel as fighters unleashed barrages of rocket and mortar fire, sending residents rushing to shelters.
Around 460 rockets and mortar rounds were fired at Israel, the most ever in such a brief time period, the army said.
An anti-tank missile hit a bus near the Gaza border that Hamas says was being used by Israel’s army. An Israeli soldier was severely wounded.
In all, some 27 Israelis were wounded, three of them severely.
A Palestinian labourer from the occupied West Bank was killed when a rocket hit a building in the Israeli city of Ashkelon.
Meanwhile, a Palestinian was killed by Israeli fire in the border area of the northern Gaza Strip, the enclave’s health ministry and a security source said.
The man killed was identified as Nawaf al-Aatar, 20, and a Gazan security source said he was fishing at the time near the border fence.
An Israeli army spokeswoman said “troops recognised a number of suspects who approached the security fence in the northern Gaza Strip”.
“When one of the suspects approached the security fence, (Israeli) troops fired toward him in accordance with the standard operation procedures,” she said.
