JERUSALEM — Prime Minister Benjamin Netanyahu of Israel said Monday that he would be willing to hand over leadership for one year to a longtime right-wing rival, Naftali Bennett, in a last-ditch effort to cobble together a new government.

Netanyahu, who has spent the last 12 years in office and is now standing trial on corruption charges, announced the offer just ahead of a deadline to form a government, in the wake of Israel’s fourth inconclusive election in two years.

The arrangement, part of a rotation agreement, would be a highly unusual one since Bennett, who served briefly as defense minister in a previous government, leads a small, pro-settlement party, Yamina, that holds just seven seats in the 120-seat Parliament.

Netanyahu wrote about the offer in a post on Facebook less than 36 hours before his time to form a new government runs out at midnight on Tuesday. Bennett appeared to dismiss the offer as political spin in his initial response.

The last election in March has left Netanyahu weakened and, so far, unable to muster a coalition that would command a parliamentary majority.

Netanyahu’s conservative Likud party won the most seats of any party in the election, securing 30 seats in the 120-seat Parliament, but had been endorsed for the premiership by only 52 lawmakers from Likud, two loyal ultra-Orthodox parties and a far-right alliance called Religious Zionism.

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Even with Bennett’s Yamina on board, Netanyahu would still be two seats short of the 61 needed to form a majority government.

Still, the support of Bennett’s party could be key, and he has been negotiating both with the Netanyahu-led bloc and with an opposition bloc made up of parties from across the spectrum that are determined to unseat Netanyahu. That group also had no easy path to power.

If Bennett were to take up Netanyahu’s offer, it is unclear how much power Bennett would actually wield given the imbalance between their respective parties.

Bennett has said he would prefer to sit in a coherent right-wing government but noted that he was waiting for Netanyahu to show he had a majority. His immediate response to Netanyahu’s offer was dismissive.

“I have just heard Netanyahu’s proposal, and I have to say it is unclear to me,” Bennett said. “I did not demand the premiership from Netanyahu, but rather I asked for a government. And that, to my regret, he does not have.”