Shock, grief and pain have cascaded across Israel since Hamas gunmen poured out of Gaza to kill an estimated 1,200 Israeli civilians and soldiers on Oct. 7. So have anger and a thirst for vengeance, which the country’s leaders are verbalizing in language that critics in Israel say often crosses the line into incitement.

“We are fighting human animals, and we are acting accordingly,” said Yoav Gallant, the defense minister, two days after the attacks, as he described how the Israeli military planned to eradicate Hamas in Gaza.

“We’re fighting Nazis,” declared Naftali Bennett, a former prime minister.

“You must remember what Amalek has done to you, says our Holy Bible — we do remember,” said Prime Minister Benjamin Netanyahu, referring to the ancient enemy of the Israelites, in scripture interpreted by scholars as a call to exterminate their “men and women, children and infants.”

Inflammatory language has also been used by journalists, retired generals, celebrities, and social media influencers, according to experts who track the statements. Calls for Gaza to be “flattened,” “erased” or “destroyed” had been mentioned about 18,000 times since Oct. 7 in Hebrew posts on X, the site formerly known as Twitter, said FakeReporter, an Israeli group that monitors disinformation and hate speech. The phrases were only mentioned 16 times in the month and a half before the war.

The cumulative effect, experts say, has been to normalize public discussion of ideas that would have been considered off limits before Oct. 7: talk of “erasing” the people of Gaza, ethnic cleansing, and the nuclear annihilation of the territory.

Incendiary statements are not limited to Israel, of course. Ghazi Hamad, a senior leader of Hamas, vowed on Oct. 24 that the group would wipe out Israel as a country, and appeared to exult in the barbaric acts that his militants had carried out against Israeli civilians. “We are not ashamed to say it with full force,” he said. “We have to teach Israel a lesson, and we will do it again and again.”

But the proliferation of such language by Israelis has opened a debate in Israel, where far-right and ultranationalist politicians were testing the boundaries of acceptable speech even before Oct. 7. Itamar Ben-Gvir, a right-wing settler who went from fringe figure to minister of national security in Mr. Netanyahu’s cabinet, has a long history of making incendiary remarks about Palestinians. He said in a recent TV interview that anyone who supports Hamas should be “eliminated.”

Concerns about the spread of extremist rhetoric are an extension of a political battle within Israel that has been raging all year between Mr. Netanyahu’s ultraright government and a civic opposition, some of whom now worry that it will inure Israelis to the civilian toll in Gaza as the war goes on.

The idea of a nuclear strike on Gaza was raised last week by another right-wing minister, Amichay Eliyahu, who told a Hebrew radio station that there was no such thing as noncombatants in Gaza. Mr. Netanyahu suspended Mr. Eliyahu, saying that his comments were “disconnected from reality.”

Mr. Netanyahu says that the Israeli military is trying to prevent harm to civilians. But with the death toll rising to more than 11,000, according to the Gaza health ministry, those claims are being met with skepticism, even in the United States, which has pressed Israel to allow daily four-hour humanitarian pauses in the combat.

Such reassurances are also belied by the language Mr. Netanyahu uses with audiences in Israel. His reference to Amalek came in a speech delivered in Hebrew on Oct. 28 as Israel was launching the ground invasion. While some Jewish scholars argue that the scripture’s message is metaphoric not literal, his words resonated widely, as video of his speech was shared on social media, often by critics.

“These are not just one-off statements, made in the heat of the moment,” said Michael Sfard, an Israeli human rights lawyer and author of “The Wall and the Gate: Israel, Palestine and the Legal Battle for Human Rights.”

“When ministers make statements like that,” Mr. Sfard added, “it opens the door for everyone else.”

Yehuda Shaul, co-director of Ofek, a think tank in Jerusalem, has collected 286 statements since Oct. 7 that he classifies as having the potential to incite unlawful behavior. His list includes Eyal Golan, an Israeli pop singer; Sara Netanyahu, the wife of Mr. Netanyahu; and Yinon Magal, a host on Israel’s right-wing Channel 14.

“Erase Gaza. Don’t leave a single person there,” Mr. Golan said in an interview with Channel 14 on Oct. 15.

“I don’t call them human animals because that would be insulting to animals,” Ms. Netanyahu said during a radio interview on Oct. 10, referring to Hamas.

“It’s time for Nakba 2,” Mr. Magal wrote on X on Oct. 7, a reference to the mass displacement and flight of Palestinians before and after Israel’s creation in 1948, which Palestinians refer to as the “nakba,” or “catastrophe.”

In the West Bank last week, several academics and officials cited Mr. Eliyahu’s remark about dropping an atomic bomb on Gaza as evidence of Israel’s intention to clear the enclave of all Palestinians — a campaign they call a latter-day nakba.

On Saturday, the Israeli agriculture minister, Avi Dichter, said that the military campaign in Gaza was explicitly designed to force the mass displacement of Palestinians. “We are now rolling out the Gaza nakba,” he said in a television interview. “Gaza nakba 2023.”

The rise in incendiary statements comes against a backdrop of rising violence in the West Bank. Since Oct. 7, according to the United Nations, Israeli soldiers have killed 150 Palestinians, including 44 children, in clashes. Jewish settlers, some of whom are armed and informally allied with the military, have killed eight people, one of them a child, according to the United Nations.

Israeli officials point out that Hamas is also active in the West Bank and say that many of those clashes resulted from the military’s efforts to root out militants. Three Israelis have been killed in attacks by Palestinians since Oct. 7.

Eran Halperin, a professor of psychology at Hebrew University in Jerusalem, argued that the use of inflammatory language by Israeli leaders is not surprising, and even understandable, given the brutality of the Hamas attacks, which inflicted collective and individual trauma on Israelis.

For the first time since the Yom Kippur War of 1973, he said, Israel’s survival hangs in the balance. The country is facing the prospect of a multi-front conflict against Hezbollah and Hamas, as well as a potential uprising in the West Bank.

“People in this situation look for very, very clear answers,” Professor Halperin said. “You don’t have the mental luxury of complexity. You want to see a world of good guys and bad guys.”

“Leaders understand that,” he added, “and it leads them to use this kind of language, because this kind of language has an audience.”

Casting the threat posed by Hamas in stark terms, Professor Halperin said, also helps the government ask people to make sacrifices for the war effort: the compulsory mobilization of 360,000 reservists, the evacuation of 126,000 people from border areas in the north and south, and the shock to the economy.

But Mr. Sfard warned that Israel’s dehumanization of the people of Gaza could open the door to further discrimination and mistreatment of Palestinian citizens in Israel. It will also make Israelis more inured to the civilian death toll in Gaza, which has isolated Israel around the world, he added. A civilian death toll of 10,000 or 20,000, he said, could seem to “the average Israeli that it’s not such a big deal.”

In the long run, Mr. Sfard said, such language dooms the chance of ending the conflict with the Palestinians, erodes Israel’s democracy and breeds a younger generation that is “easily using the language in their discussion with their friends.”

“Once a certain rhetoric becomes legitimized, turning the wheel back requires a lot of education,” he said. “There is an old Jewish proverb: ‘A hundred wise men will struggle a long time to take out a stone that one stupid person dropped into the well.’”

Adam Sella contributed reporting.