Lieberman also said that his party will quit the government as a result of his resignation, leaving Netanyahu with a narrow majority in parliament. The opposition parties joined his call. His right-wing party, Yisrael Beiteinu, will also leave the ruling coalition.
Elections are not due until November 2019, but Lieberman's resignation increases the likelihood of an earlier vote.
"Were I to stay in office, I would not be able to look southern residents in the eye", Lieberman told reporters, referring to Israelis subjected to a surge in Palestinian rocket attacks before Tuesday's truce took hold. Hamas, in turn, had scaled back its mass protests that have led to weekly bloodshed along the Israeli border.
The former foreign minister received the defence portfolio in May 2016. "But together with the heads of the security forces, I see the overall picture of Israel's security, which I can not share with the public", he said at a ceremony to commemorate David Ben-Gurion, Israel's first prime minister.
"I see the big picture of Israeli security that I can not share with the public", he said.
For these and many other Israelis, accepting the ceasefire was an act of cowardice, that gives precedence for Hamas and Islamic Jihad to terrorize Israel whenever they please. I can not detail our plans for the future. "I can not elaborate on our plans for the future", he said, "We will determine the right conditions and the right times for the State of Israel, which are correct for the security of our citizens".
"In times like these, leadership is not doing the easy thing".
The Israel-Gaza frontier remained quiet overnight.
Palestinians survey the rubble from a destroyed residential building hit by Israeli airstrikes in Gaza City on Tuesday. Both sides appear reluctant to launch a full-scale war.
The Gaza health ministry said at least three Palestinians, including two militants, were killed in the Israeli strikes.
The Egyptian-brokered truce was announced by Gaza militant groups, including Hamas, on Tuesday.
Demonstrators each week approach the border fence, throwing firebombs, grenades and burning tires at Israeli troops. The sad truth is that the Jewish-Israeli public is only really divided over the degree of violence to be used against the Palestinians - all while keeping the status quo intact. Israel says it is defending its border against attackers, but it has come under heavy worldwide criticism for shooting unarmed people.
United Nations and Egyptian mediators had been making progress in recent weeks toward informal understandings between Israel and Hamas that would ease the blockade in exchange for ratcheting down the border protests.
Israelis learned about the latest Gaza ceasefire following a two-day, 500-rocket barrage from the likes of Hamas and Al Jazeera.
Lt. Col. Jonathan Conricus, an IDF spokesman, said the army had sent reinforcements to the Gaza frontier and bolstered its Iron Dome missile defense system.
"It only lets us suffer, nothing more".
Meanwhile, crowds of Palestinians have gathered in various places in the Gaza Strip to celebrate what they call "the victory of the resistance", where candies were distributed in the streets and Palestinian flags were flown. Confronted by such hawkish responses from political adversaries right and left, Netanyahu might feel forced to initiate some sort of military action, either in Gaza, the West Bank, or on the northern front vis-à-vis Iran in Syria, or Hezbollah in Lebanon.
The military said it struck some 160 targets in the enclave.
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