A closed-door UN Security Council meeting on Tuesday ended with no agreement on how to address days of significantly escalated violence in the Gaza Strip after it ended in a fragile ceasefire, diplomats said.
"I hear the voices of the residents of the south".
Liberman called the PM's Gaza Strip policy "defeatist", charging that "What we are now doing as a country is to buy a short-term quiet at the expense of long-term national security".
Lieberman, a security hardliner, heads the right-wing Yisrael Beitenu party, which holds five seats in the 120-seat Knesset, or parliament.
"There's no obligation to go to an election in this time of security sensitivity", the official said on condition of anonymity.
Liberman also said there's a need to quickly reach a date for the next elections, and that he hoped that a meeting to decide the date be held no later than Sunday.
The deal has provoked criticism from within Netanyahu's government as well as from Israelis who live near the Gaza Strip and want further action against its Islamist rulers Hamas.
Wednesday's incident marked the first unrest since Hamas and other militant groups in Gaza accepted an Egyptian-brokered cease-fire to end two days of intense fighting with Israel that had pushed the sworn enemies to the brink of another war.
But as defense minister, he could be no less a thorn in Netanyahu's side than Lieberman.
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His resignation delivers a major blow to Netanyahu's coalition government and sparked immediate calls for early elections.
Since March 30, more than 200 Palestinians have been martyred by Israeli army gunfire - and thousands more injured - while taking part in rallies along the Gaza-Israel buffer zone.
"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 in honor of Israel's founding father David Ben-Gurion.
Palestinian officials said seven people were killed inside Gaza by Israeli air strikes, while a Palestinian working in Israel died when one of the rockets launched by militants struck his bedroom.
Announcing his decision in a news conference, which takes effect 48 hours after he puts it in writing, Lieberman deemed Tuesday's Egyptian-mediated deal with the Palestinian group Hamas "a capitulation to terror".
With air raid sirens wailing throughout southern Israel and the explosions of airstrikes thundering in Gaza, the two sides had appeared to be on the verge of their fourth war in a decade.
Netanyahu today defended his decision to invoke the ceasefire, saying that Hamas "begged" for a ceasefire and "they know very well why", the Jerusalem Post reported.
In total, at least 15 Palestinians and one Israeli have been killed between Sunday and Tuesday.
Palestinian militants responded with heavy fire on southern Israel, launching almost 400 mortar rounds and rockets that wounded 27 people and killed one - a Palestinian living in southern Israel.