TEL AVIV—Israeli Prime Minister Benjamin Netanyahu is trying to rally his right-wing base against a new ruling coalition that includes, for the first time in the country’s history, an independent Arab party that would have a role in shaping the policies of the predominantly Jewish state.

Less than an hour before a midnight Wednesday deadline, Naftali Bennett, who heads the right-wing Yamina party, and Yair Lapid, who leads the centrist Yesh Atid party, agreed to form a coalition government that would dislodge the incumbent. The coalition would include six other parties from across the political spectrum, including one of Israel’s Arab parties, Ra’am.

The coalition, if approved by the Knesset, would be the most ideologically diverse in Israel’s history. But Mr. Netanyahu, in a jab to his right-wing rival, accused Mr. Bennett of giving in to Ra’am’s demands, especially regarding the relaxing of policies aimed at preventing illegal building by Arab communities in the Negev Desert region in southern Israel.

“Bennett sold the Negev to Ra’am,” Mr. Netanyahu tweeted Thursday. “Every lawmaker voted in by right-wing votes must oppose this dangerous left-wing government.”

Mr. Netanyahu was raising an issue that is highly sensitive, and often divisive, among the country’s Jews and Arabs. Unsanctioned house-building by Muslim Arabs in the Negev Desert is opposed by many in the right-wing camp, who accuse the communities there of illegally seizing large tracts of land. The Bedouin communities that live in the Negev Desert insist that they have been forced to build illegally because the state hasn’t provided sufficient permits to settle on what they say is their ancestral land.

The accusation is part of Mr. Netanyahu’s last-ditch attempt to convince some right-wing lawmakers to abandon the coalition. Pushing back, Mr. Bennett’s Yamina party said they had agreed to far less with Ra’am than did Mr. Netanyahu himself.

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Mr. Netanyahu was the first to get the mandate to form a government after inconclusive elections in March—the country’s fourth since 2019—and also talked with Ra’am about joining his coalition. Mr. Netanyahu has previously said he was planning to recognize some unsanctioned construction by the Bedouin in the Negev. He failed to form a coalition.

The new coalition of eight political parties agreed to a last-minute deal on Wednesday, but have yet to disclose the full terms of that agreement.

As part of their understanding, Mr. Bennett would serve first as prime minister for two years followed by Mr. Lapid. The rotation appears to be aimed at right-wing Jewish Israelis who previously supported Mr. Netanyahu’s governments but now see in Mr. Bennett a break from the country’s longest-serving prime minister, who faces a corruption trial. Mr. Netanyahu denies all wrongdoing.

Until the government is sworn in, Mr. Netanyahu can still try to undo the coalition deal. The defection of just one or two lawmakers could prevent the new coalition from mustering a majority and force another election—what would be the country’s fifth since 2019.

Mr. Netanyahu’s supporters, including lawmakers from his right-wing Likud party, have gone all out to convince some right-wing lawmakers to abandon the prospective coalition.

“There is great pressure being exerted against Yamina lawmakers, on social media, through private phone calls and protests by their homes—it is crossing lines,” said Yamina lawmaker Matan Kahana, in an interview with Kan news Thursday morning.

Mr. Netanyahu met Thursday with leaders of settlements in the West Bank along with heads of right-wing parties still aligned with him in an effort to expand the pressure campaign.

Chairman of the Kiryat Arba Local Council Eliyahu Libman, who participated in the meeting, said Mr. Netanayhu urged settler leaders to pressure Mr. Bennett and his party members because the settlers would suffer under the new government.

Yamina lawmaker Nir Orbach tweeted late Wednesday “We will not abandon the Negev. Period.”

Mansour Abbas, leader of the Islamist Ra’am party, in an interview with Army Radio on Thursday, said the coalition was seeking to expand its support to make up for the potential loss of any right-wing lawmakers under pressure by Mr. Netanyahu. He said such additional support may come from fellow Arab lawmakers from a different party. Mr. Bennett’s Yamina party said Thursday that it would reject such support from the other Arab parties.

Aside from their common goal to unseat Mr. Netanyahu, parties in the new coalition have ideologically little in common. Messrs. Bennett and Lapid would face the challenge of keeping their fractious government together for more than a few months if sworn in.

Left-wing lawmakers on Thursday touted parts of their coalition agreement that included legislation to improve rights for same-sex couples. But Mr. Abbas’s Islamist party is staunchly opposed to such legislation.

“The glue [for this coalition] is agreements on issues where there’s a consensus,” said Mr. Abbas. “To deviate from this can weaken the coalition and God forbid in the future even topple it.”