Netanyahu rival quits war cabinet, leaving Israel between far-right support and Gaza cease-fire.

• Israel's war cabinet minister Benny Gantz resigned from the emergency government,.
• After Netanyahu failed to present a concrete plan for the Gaza enclave's post-war governance by the June 8 deadline, he withdrew his party from the coalition.
• Unfortunately, Netanyahu is hindering our progress towards true victory, which justifies the ongoing and painful cost of war. As a result, we are departing from the emergency government with a heavy heart but with complete certainty.

Benny Gantz, Israel's war cabinet minister, resigned from the emergency government, potentially strengthening Prime Minister Benjamin Netanyahu's far-right support base and making it harder to achieve a cease-fire in Gaza.

Gantz, a former Israeli Defense Forces chief of staff and centrist politician, founded and led the National Unity party, which joined Netanyahu's emergency government following the Gaza war. However, Gantz withdrew his party from the coalition after Netanyahu failed to present a concrete plan for the Gaza enclave's post-war governance by the June 8 deadline.

Netanyahu previously proposed "day-after" measures for the Gaza Strip that emphasized Israel's "security responsibility" over the territory and rejected the idea of dividing it into a separate Palestinian state.

On Sunday, Gantz announced his resignation while Netanyahu celebrated the rescue of four hostages taken by Hamas during the Oct. 7 terror attack, which led to Israel's Gaza campaign.

Unfortunately, Netanyahu is hindering our progress towards true victory, which justifies the ongoing and painful cost of war. As a result, we are departing from the emergency government with a heavy heart but with complete certainty.

Gantz stated, "I was privileged to bring all our experience to the cabinet room with my friends. I know others are there too. The Defense Minister Yoav Gallant and the prime minister are aware of what needs to be done. I hope they will adhere to their plan, and everything will be fine."

On Saturday, Netanyahu urged Gantz to remain in the emergency government, emphasizing the need for unity rather than division, as translated by Google.

The decision of Gantz and Eisenkot to leave the emergency government was welcomed by Yair Lapid as "important and right."

"It's time for a new government in Israel that will restore security, return abducted citizens, and revive the country's economy and international standing," Lapid stated in a Google-translated social media post.

Gantz's withdrawal poses a challenge to Netanyahu's government, which is facing criticism over its handling of the Gaza conflict and the treatment of hostages. Israel has been criticized for its military response and the risk to Palestinian civilians, including a UN order to halt the war campaign in Rafah and an ICC prosecutor's request for arrest warrants against Netanyahu, Gallant, and three Hamas leaders.

Since the start of the Gaza conflict, Israeli official figures claim that approximately 1,200 people have been killed, while Gaza's Ministry of Health reports a death toll of 37,000 in the enclave.

The departure of Gantz will cause some turbulence, but not dismantle the Netanyahu administration. According to Eran Etzion, the former deputy head of Israel's National Security Council, Netanyahu can rejoin his coalition of far-right and ultra-Orthodox parties.

Netanyahu will continue to maneuver between his base and US demands to maintain power, while the pro-democracy movement will increase its pressure in the streets. Additionally, the highly unpopular "draft law" is expected to further delegitimize the government, according to Etzion.

Nimrod Goren, a senior fellow at the Middle East Institute, stated to CNBC that Netanyahu is unlikely to go against his far-right coalition partners at this time, which decreases the chances of Israel endorsing a cease-fire proposal in the Gaza Strip, such as the three-phase plan publicly aired by the U.S. last month.

Goren stated that Gantz's resignation decreases the likelihood of Netanyahu agreeing to a deal that requires a substantial pause in IDF operations in Gaza and the release of a substantial number of Palestinian prisoners.

The far-right politicians have criticized the framework, with Itamar Ben-Gvir, the national security minister and leader of the Jewish Power Party, calling it a "promiscuous deal" that benefits terrorism and poses a security risk to Israel in a Google-translated social media post. He also threatened to dissolve the government if the proposal is implemented.

Likewise, Bezalel Smotrich, the finance minister and leader of the Religious Zionist Party, stated that he would not participate in a government that would approve the proposed plan and end the war without destroying Hamas and returning all the abductees, as per a Google-translated social media update.

Gantz's departure will not affect the cease-fire proposal, according to Etzion.

"Gantz's stance on the deal was the same as Netanyahu's, as both leaders have assured their support for the proposition. The decision was ultimately up to Netanyahu, who could gather a majority for any choice he made. This was true when Gantz was in power and remains true now that he has stepped down."

CNBC has reached out for comment to the Israeli Prime Minister's Office.

— CNBC's Dalya Al Masri contributed to this report.