Prime Minister Benjamin Netanyahu said on Sunday that he was taking action to oust the director of the Shin Bet, Israel’s domestic intelligence agency, raising concerns among critics that he was seeking to undermine its independence.

Mr. Netanyahu’s effort to fire Ronen Bar, the head of the powerful agency, underscored longstanding tensions between the prime minister and leading members of Israel’s security establishment, who have clashed over the handling of the war in Gaza.

The decision to pursue Mr. Bar’s termination also came in the wake of Shin Bet investigations into allegations against several Netanyahu aides, including that one allegedly leaked a secret document to a foreign newspaper.

The prime minister’s office said that Mr. Netanyahu had informed Mr. Bar that a draft resolution for his ouster would be presented to the Israeli cabinet this week for approval.

But in a letter, Gali Baharav-Miara, the attorney general, said Mr. Netanyahu wasn’t allowed to even begin the process until a determination was made about the legality of terminating Mr. Bar. She said there were concerns that it would be a conflict of interest for Mr. Netanyahu.

Members of Mr. Netanyahu’s coalition have demanded the prime minister fire Mr. Bar for what they say is his undermining of the prime minister. They have also called for firing Ms. Baharav-Miara, who has long had a strained relationship with Mr. Netanyahu.

Any decision to remove Mr. Bar, who has led the agency since 2021, would also probably be appealed to the Supreme Court.

In a recorded video message posted on social media, Mr. Netanyahu said the firing was necessary because he didn’t trust Mr. Bar.

“At any time — especially during an existential war like this one — there must be complete trust between the prime minister and the director of the Shin Bet,” he said.

Mr. Bar fired back with a strongly worded public statement, saying Mr. Netanyahu’s expectation of “personal trust” was in opposition to the public’s interests.

“It’s a fundamentally flawed expectation that is in contravention with the Shin Bet law and statesmanship,” he said in a rare public statement.

Mr. Bar said he had previously told Mr. Netanyahu that he planned to stay in his post until the return of all hostages held in Gaza and the completion of a number of sensitive investigations. He also said he wanted to finish preparing two people whom he described as candidates to succeed him.

The move to terminate Mr. Bar followed the removal in the last several months of two other security leaders who were often at odds with the prime minister: the defense minister and the Israeli military’s chief of staff.

Former members of the Shin Bet have raised concerns about the possibility of Mr. Netanyahu’s nominating a successor to Mr. Bar based on political considerations.

“Israeli democracy is on a crash course,” said Ami Ayalon, a former head of the Shin Bet. If the prime minister manages to oust Mr. Bar, it would be “another step toward turning Israel into a state that prioritizes personal loyalty to the leader above all else,” he said.

This month, the Shin Bet publicized a summary of its inquiry into agency failures before and during the Hamas-led October 2023 attack that was critical of both Mr. Netanyahu’s government and the agency. While the summary acknowledged the Shin Bet had failed to provide a warning of the attack, it said it had warned that Hamas had not been deterred in preceding months and had recommended taking action against the militant group.

The report also said the Shin Bet had informed the government that political divisions in Israel had emboldened its adversaries, putting the country in a vulnerable position. This finding was widely seen as pointing a finger at Mr. Netanyahu’s government, which had pushed a controversial judicial overhaul that divided the Israeli public.