Binyamin Netanyahu's cabinet is in disarray as the Israeli prime minister comes under fire from several of his most senior ministers for his handling of the crisis in Gaza.

The storm of public criticism from within his own ranks led to the sacking on Tuesday night of the deputy defence minister, Danny Danon, a member of Netanyahu's Likud party.

Danon had told the media that Hamas had humiliated Israel by setting conditions for peace, after Netanyahu said he was willing to accept the Egyptian-brokered ceasefire. Hamas claimed that it had not been consulted over the ceasefire conditions and rejected it.

"At a time when … Israel and the IDF [Israeli Defence Forces] are in the midst of a military campaign against the terrorist organisations and taking determined action to maintain the security of Israel's citizens, it cannot be that the deputy defence minister will sharply attack the leadership of the country regarding the campaign," Netanyahu said in a statement on Tuesday.

"These sharp remarks on the deputy defence minister's part are irresponsible, especially given his position. They also serve the Hamas terrorist organisation as a tool to attack the government with."

The divisions within the Israeli cabinet have been mocked by Hamas, with spokesman Fauzi Barhoum calling the sacking of Danon a "victory for the resistance".

Avigdor Lieberman, Israel's hawkish foreign minister, split his Yisrael Beiteinu party from Likud – dismantling a crucial alliance for Netanyahu – having accused the prime minister of hesitation over Gaza.

Lieberman criticised the government for accepting the Egyptian-brokered ceasefire and called for an IDF ground assault and occupation of the Gaza Strip, arguing that a ceasefire would allow Hamas and other Palestinian militant groups to replenish their stock of weapons.

"All this hesitation works against us. We must go all the way, there is no alternative. We have to end this conflict with the IDF in control of all of Gaza … There is no other way to tackle the Hamas and Islamic Jihad terror that rules Gaza," Lieberman said at a press conference on Tuesday night.

Netanyahu's election last year was only possible at the head of a shaky coalition of rightwing parties, cracks in which appear to be emerging over the war in Gaza.

Danon and Lieberman are not Netanyahu's only critics. Israeli media reported that another senior figure on the Israeli right, Naftali Bennett, who leads the Jewish Home party, also voted against a ceasefire. Haaretz has reported both Lieberman and Bennett as claiming the government had not informed them about the ceasefire, and that they had heard about the proposed deal via the media.

Analysts have said the spats between Netanyahu and his rightwing cabinet colleages should be seen within the broader framework of Israel's shaky coalition dynamics. Michael Stephens, the deputy director of Qatar-based thinktank Rusi, said that the divisions were extremely damaging to the Israeli government.

"[The Lieberman] brand of rightwing populism is actually hurting Bibi more than he initially thought. Lieberman was always a threat but the thinking was Likud-Beitenu would contain him. Now it's more clear that the right in general is fractured, and particularly at odds with the security establishment."

Hugh Lovatt, the Israel/Palestine project coordinator at the European Council on Foreign Relations, said the split could "help to balance out the ruling coalition and glue it around Netanyahu" as more extreme voices gave way to centrist elements of the government, such as justice minister Tzipi Livni, who have called for greater restraint on Israel's part and a greater willingness to secure a ceasefire with Hamas.

"As far as Danny Danon is concerned, he is increasingly seen as a potential rival to Netanyahu within his own party and has been gaining increasing popularity. Netanyahu's [sacking of him] may backfire. Now that Danon is out of the cabinet he will have even more freedom to criticise him," Lovatt said.

Four rockets were shot down over Tel Aviv at around 9am on Wednesday morning, with reports of shrapnel falling in the north of the city. Israel also suffered its first casualty on Tuesday, when a civilian was killed by a mortar shell outside the Erez crossing into Gaza. The Palestinian death toll now stands at 205, with Israel warning 100,000 Palestinians to leave their homes on Wednesday ahead of further aerial bombardments of the strip.