Binyamin Netanyahu could face the electorate as early as February after he rejected a demand from Naftali Bennett, his coalition ally, to be appointed defence minister as a condition of his continuing political support.
Within minutes, a statement from Likud said that was incorrect.
Contradicting the initial reports, Israeli media said that Netanyahu put out a statement claiming the rumor was false, saying that he will take on the role of defense minister and warned of toppling a right-wing government.
It added that early next week the premier would consult leaders of the coalition parties.
Netanyahu also spoke by phone with his coalition partners, urging them to "make every effort not to bring down the right-wing government" and to prevent the left from getting into power, the spokesperson said.
Lieberman announced his resignation in a press conference on Wednesday, citing sharp disagreement over an agreed cease-fire between Israel and Hamas, the Islamist Palestinian movement that runs the Gaza Strip.
Yehiyeh Sinwar, Hamas leader in Gaza, told the crowd that Abu Obaida, Hamas' armed wing spokesman, had said the group will respond to any bombardment by Israel by expanding the range of its rocket fire.
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This could be the final decision of the tribunal, officially called the Extraordinary Chambers in the Courts of Cambodia (ECCC). There are parts of the country where victims and perpetrators live side by side in villages.
They called for tougher action against Hamas which has portrayed the ceasefire and Lieberman's resignation as a victory. Instead, Netanyahu himself will serve as acting defense minister for the time being, in addition to his duties as prime minister and acting foreign minister.
"The chances of stopping this speeding train appear impossible, but Netanyahu is still trying". Without Liberman's Yisrael Beitenu party, Netanyahu's ruling coalition only had a one-seat majority in the Knesset.
The meeting between Netanyahu and Bennett, who is the head of the far-right Habayit Hayehudi party (Jewish Home), was held amid the government's calls to avoid snap elections.
"There is a solution".
Finance Minister Moshe Kahlon, the head of the center-right Kulanu Party, has said it is an economic must to have elections as early as possible. The raid led to two days of intense cross-border fighting. If this is indeed the case, it is expected elections will be held between March and May 2019.
Analysts say the prime minister would be better positioned to fight any charges with a fresh mandate from the voters.