Netanyahu has come under public criticism after meeting the families of captives released from Gaza's Nuseirat Refugee Camp and not meeting the relatives of captives released in swap deals earlier in the war, as well as bereaved families.
Yair Lapid told Kan, Israel's public broadcaster, that "if you are the prime minister – you are the prime minister of both successes and failures".
"Disappearing when things don't go your way is disgraceful, but is this something we didn't know about before?," he added.
Izhar Shay, whose son was killed during Hamas' 7 October attack on Israel, was quoted by the Times of Israel as saying: "I despise him [Netanyahu], wretched man."
"I am one of those bereaved parents who the prime minister did not bother to call," he said, adding that a "moral and honorable prime minister would have called to comfort and give strength. And to apologize that it happened on his watch".
Following the rescue of four Israeli captives amid an Israeli massacre of Palestinians in Nuseirat, Netanyahu met all four captives, Noa Argamani, Almog Meir Jan, Andrei Kozlov and Shlomi Ziv.
He later held a press conference where he said vowed to bring home the remaining captives, and "do whatever it takes to get them all back home."
He also implored to war cabinet member Benny Gantz to remain in the government after the latter had threatened to leave unless Israel set a roadmap to end the war.
Several Israeli publications also ran articles criticizing Netanyahu's use of the hostage release to improve his image.
This includes Haaretz journalist Yossi Verter, who wrote that as well as not changing Israel's predicament in Gaza, Netanyahu has not called any of the hostages previously released under a deal with Hamas, or hostages who were killed in Gaza.
"That is the kind of unprincipled, cynical and malicious leadership of the person still occupying the prime minister's office," he wrote.
"Netanyahu approved the operation; if, God forbid, it had ended differently, with the deaths of the hostages and additional soldiers, would he have faced the cameras?" he questioned.
Commenting on Netanyahu's visit to craptives and calls for Gantz to stay in the government Israeli columnist Ben Caspit wrote in Walla News that he "needs partners only to share the price, not the goods."
Tens of thousands of Israeli's took to the streets in demonstrations yesterday following the operation, with protesters in Jerusalem demanding a hostage deal and protesters in Tel Aviv calling for new elections.
Yakov Argamani, the father of Noa, urged the public to demonstrate for the hostages in Tel Aviv, while Einav Zangauker, whose son Matan is still held in Gaza, called on the government to sign a deal for the release of the remain captives held in Gaza.
Some 116 Israelis remain in Gaza, although the Israeli military believes that at least 41 are dead. Many have been killed by Israeli airstrikes or during previous Israeli rescue attempts.
The Israeli operation, which took place in Gaza's Nuseirat Refugee Camp, resulted in the killing of 274 Palestinians and the wounding of around 698 others, according Gaza's health ministry.
Israel's war on Gaza, which is in its ninth month, has killed 37,084 Palestinians, with a further 84,494 wounded.