In the afternoon, in a televised news conference, Mr. Netanyahu triumphantly announced the new deal, under which the office of the United Nations High Commissioner for Refugees committed to persuading countries in the West to take at least 16,250 migrants over five years, while Israel would grant official status as temporary residents to most who remained.
Estimates of the population of African asylum seekers in Israel, mostly from Eritrea and Sudan, range from 35,000 to 39,000.
But the agreement to let many stay in Israel drew harsh criticism from some of Mr. Netanyahu’s right-wing coalition allies, who were taken by surprise. Naftali Bennett, the education minister and leader of the far-right Jewish Home party, said the deal would “turn Israel into an infiltrator’s paradise.”
Mr. Netanyahu backtracked.
In a late-night Facebook post he said he was “attentive” to critics and wanted to explain the sequence of events. Rwanda, he said, had withdrawn from its agreement with Israel under pressure from the New Israel Fund — a nonprofit organization that promotes liberal democracy in Israel and is loathed by the right wing here — and “elements in the European Union.”
He said he was suspending the deal with the United Nations refugee agency pending a meeting on Tuesday morning with the veteran residents of south Tel Aviv, where many of the African migrants are concentrated, and that he would then review the understandings reached with the agency.
The European Union’s delegation in Israel was incredulous.
“Guess it’s just one of those days,” the delegation wrote on Twitter. “At 20:57 you congratulate #Israel & @refugees on their agreement, at 21:46 you like @IsraelMFA announcement on the deal, at 22:50 the PM suspends it and blames, among others, #EU (where #UNHCR hoped to resettle significant number of refugees).”
The New Israel Fund accused Mr. Netanyahu of lying, saying the organization, which has offered support for the asylum seekers in Israel, “had nothing to do with Rwanda’s decision to refuse to participate in the Prime Minister’s cruel mass deportation plan.”
“It is pathetic, shameful, and a stain on Israel in the global arena that the Prime Minister would blame Israel’s human rights defenders for his ineptitude and his immoral policies,” the New Israel Fund said in a statement.
Earlier, at the news conference, Mr. Netanyahu revealed details of the new deal.
“The agreement states that for every person who leaves, one will stay,” he said, noting that the refugee agency would be financing the departure. “I think it’s a good solution, a proper solution.”
The plan was to be carried out in three phases, with the first 6,000 migrants expected to leave over the next 18 months.
William Spindler, a spokesman for the United Nations refugee agency in Geneva, said there was no agreement in place with other countries to take any of them. He said that the agency would need countries to come forward with offers, but that “we are confident we will be able to find places for these 16,000 people.”
Such promises can be hard to keep. The European Union is still struggling to get member countries to honor a 2015 agreement to take migrants from the Middle East, Africa and Asia.
Mr. Netanyahu explained to the Israeli public that he had come to the arrangement with the United Nations after it became clear that sending the migrants to Rwanda was no longer an option. “We were in a catch,” he said, “meaning they would all have remained here.”
In addition, in response to petitions by Israeli human rights advocates, Israel’s High Court of Justice issued an emergency injunction last month, instructing the state to suspend its plan to begin deporting single adult men on April 1.
As part of the new plan, the Israeli government and the United Nations refugee agency said they would encourage a more balanced distribution of the asylum seekers who remain in Israel. That effort would include vocational training, job placement, and help with integrating into new communities.
The issue of the African asylum seekers has long roiled Israeli society.
From 2005 until 2012 about 60,000 surreptitiously crossed into Israel over the once-porous border with Egypt. Under international conventions, Eritrean and Sudanese asylum seekers could not be sent back to their home countries, where they could face persecution.
Anger built up among many longtime residents of south Tel Aviv, who complained that the migrants had brought crime and made their neighborhood unlivable. Other Israelis volunteered to help the migrants. Many passed through a remote detention center in the Negev desert.
The government stopped the flow by building a steel barrier along the border and by making life for the migrants in Israel increasingly uncertain and uncomfortable. Few asylum seekers have received refugee status. Government ministers routinely call them “infiltrators” and economic migrants who threaten Israel’s future as a Jewish state.
At least 20,000 have left Israel, and Mr. Netanyahu said he had made it his mission to deport the rest.
But when the Israeli government announced the plane ticket-or-prison policy three months ago, it caused a popular outcry, with many Israelis arguing that forced deportation contradicted Jewish values. Newspapers filled with petitions signed by Israeli doctors, pilots, rabbis, musicians and Holocaust survivors, all opposing the policy.
Stickers appeared in pubs, cafes and other establishments saying, “This business opposes the expulsion of asylum seekers,” and citing biblical verses like Leviticus 19:34: “The stranger who resides among you shall be to you as one of your citizens; you shall love him as yourself, for you were strangers in the land of Egypt.”