Neither Eliyahu or his party leader are in the streamlined ministerial forum running the Gaza war. Neither would they have inside knowledge of Israel's nuclear capabilities - which it does not publicly acknowledge - or the power to activate them.
"Eliyahu's statements are not based in reality. Israel and the IDF (military) are operating in accordance with the highest standards of international law to avoid harming innocents. We will continue to do so until our victory," Netanyahu's office said.
Some 9,500 Palestinians have been killed in the war, stirring widening international concern at Israel's tactics.
In a social media post, Eliyahu said: "It is clear to anyone who is sensible that the nuclear remark was metaphorical."
But he added: "A strong and disproportionate response to terrorism is definitely required, which will clarify to the Nazis and their supporters that terrorism is not worthwhile."
A spokesperson for Hamas, an Islamist group that advocates Israel's destruction, said Eliyahu represented the "unprecedented criminal Israeli terrorism (that) constitutes a danger to the entire region and the world".
In Eliyahu's Kol Barama radio interview, it was noted that ravaging Gaza would endanger some 240 hostages - among them foreigners as well as Israelis - held since Hamas sparked the war with an Oct 7 cross-border assault that killed 1,400 people.
"In war, you pay a price," the minister responded, while adding that he was praying for the hostages' return.
Benny Gantz, a centrist ex-general who joined the conservative Netanyahu from the opposition in the streamlined war cabinet, said Eliyahu's remarks had been damaging "and, even worse, added to the pain of the hostages' families at home".