Prime Minister Benjamin Netanyahu on Sunday publicly accused the head of Israel’s domestic security agency of lying to the country’s top court, the latest twist in a legal battle over Mr. Netanyahu’s attempt to fire the security chief, Ronen Bar.

In an acerbic 13-page affidavit defending his decision to remove Mr. Bar, who leads the Shin Bet, Mr. Netanyahu sought to rebut stunning allegations that Mr. Bar made against the prime minister in an equally scathing affidavit that Mr. Bar submitted last week to Israel’s Supreme Court.

The extraordinary exchange of recriminations came as part of a case brought by Israeli watchdog organizations and opposition parties against Mr. Netanyahu’s decision to oust Mr. Bar, with his government’s full approval, citing a lack of trust between them.

Mr. Bar has said that the decision to remove him stemmed not from professional considerations, but from “an expectation of personal loyalty.”

The case has roiled Israel, epitomizing a long-running domestic crisis that pits Mr. Netanyahu’s hard-line, right-wing supporters against more liberal Israelis over the balance of power between branches of government and the character of Israeli democracy.

To be able to rule on the validity of Mr. Bar’s ouster, the court might now have to decide which conflicting affidavit is more credible. Alternatively, the justices could strive for a compromise, with an agreed-upon date for Mr. Bar to step down.