A history-making vote, but with a perilously thin margin.

The political fate of Israel’s longest serving leader, Benjamin Netanyahu, is set to be decided on Sunday afternoon, when Parliament will hold a vote of confidence in a new government that would topple Mr. Netanyahu from power for the first time in 12 years.

Mr. Netanyahu’s opponents hope that the vote, if it passes, will ease a political stalemate that has produced four elections since 2019 and left Israel without a state budget for more than a year. It will also end, at least for now, the dominance of a politician who has shaped 21st-century Israel more than any other, shifted its politics to the right and overseen the fizzling of Israeli-Palestinian peace negotiations.

Mr. Netanyahu is set to be replaced by his former chief of staff and now political rival, Naftali Bennett. A former high-tech entrepreneur and settler leader, Mr. Bennett opposes a Palestinian state and believes Israel should annex much of the occupied West Bank.

If confirmed by Parliament, Mr. Bennett would lead an ideologically diffuse coalition that is united only by its antipathy toward Mr. Netanyahu. The bloc ranges from the far left to the hard right and includes — for the first time in Israeli history — an independent Arab party.

On Sunday, one hard-right lawmaker was considering whether to resign from his party, but still vote for the coalition. And an Arab lawmaker was debating whether to abstain in the vote.

If it holds, the coalition will control just 61 of Parliament’s 120 seats, and its fragility has prompted many commentators to wonder whether it can last a full term. Should it hold until 2023, Mr. Bennett will be replaced as prime minister by Yair Lapid, a centrist former television host, for the remaining two years of the term.

The parliamentary session to confirm the new government is scheduled to begin at 4 p.m. local time. Mr. Bennett is expected to speak first, followed by Mr. Lapid and then Mr. Netanyahu.

Parliament is then expected to vote for a new speaker — likely to be Mickey Levy, from Mr. Lapid’s centrist party — and finally for the government itself. If the vote passes, the government will be sworn in immediately, formally replacing Mr. Netanyahu’s administration.