"What happened yesterday –- the truce combined with the process with Hamas -- is capitulating to terror. It has no other meaning," 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."
Lieberman also said his party was leaving Prime Minister Benjamin Netanyahu's coalition, leaving the premier with only a one-seat majority in parliament, AFP reported.
Elections are not due until November 2019, but Lieberman's resignation increases the likelihood of an earlier vote.
Lieberman, a security hardliner, heads the right-wing Yisrael Beitenu party, which holds five seats in the 120-seat Knesset, or parliament.
Netanyahu has defended Tuesday's ceasefire deal that ended the worst escalation between Israel and Palestinian militants in Gaza since a 2014 war.