If Netanyahu is ousted, he could still lead the Likud party.

It isn’t just the leadership of the country that will be decided on Sunday afternoon. The confidence vote could ultimately also affect who leads Mr. Netanyahu’s right-wing Likud party.

Mr. Netanyahu has led the party for all but six of the last 28 years — 15 of which he has spent as prime minister. If he loses the vote on Sunday, he intends to continue in the post as leader of the opposition, Aaron Klein, a senior adviser to Mr. Netanyahu, confirmed in a phone interview.

But his rivals may not go along with that.

Once Mr. Netanyahu leaves government office, his authority over rivals for the party leadership will diminish because he can no longer promote party allies to coveted ministerial positions, or demote rivals. That will give greater momentum to internal critics who feel the party could have remained in office had Mr. Netanyahu stepped down from the leadership earlier and allowed a colleague to take over.

Three rival right-wing parties might have joined forces with Likud, giving the party a majority in Parliament, had Mr. Netanyahu not been in charge. The three parties were all led by former Likud members who were either former aides or allies of the prime minister, but who fell out with him personally.

Leadership of the party, which has governed Israel for 32 of the past 44 years, is seen as one of the country’s most prestigious roles.

But to oust Mr. Netanyahu from the party leadership, his rivals would have to defeat him in an internal primary in which the 120,000 Likud members would have the final say. Possible challengers include Yuli Edelstein, the health minister; Nir Barkat, a former mayor of Jerusalem; Israel Katz, the finance minister; and Danny Danon, chairman of Likud’s international branch. Recent polls have suggested that Yossi Cohen, who was until earlier this month the director of Mossad, the Israeli intelligence agency, would be the most popular candidate among Likud members.

In recent days, Israeli news outlets, citing anonymous sources, have written that Mr. Edelstein plans to run against Mr. Netanyahu, a claim Mr. Edelstein has not denied. Mr. Barkat held a rally in Tel Aviv on Thursday, nominally to discuss political policy. But commentators interpreted it as a thinly veiled statement of his leadership ambitions.

The likelihood of a challenge to Mr. Netanyahu depends on how long party colleagues expect the new government to stay in office, said Mr. Danon, who has not yet decided whether he will mount his own leadership bid.

“Within the Likud, people will look at the government to see if it’s functioning or not functioning,” Mr. Danon said. “If the feeling will be that it’s not going to last, I think his position will be stronger. But if they will actually be able to work together and to survive, I think it will be more challenging.”