The new formula reportedly will take up to five years to implement, and will include a plan to improve the living conditions in southern Israel, as well as redistribute the African population throughout Israel. The U.N. refugee agency said it could not immediately comment on the matter, but a spokeswoman said it would release a statement later in the day.
The spokesperson said to date, there has been no commitment to increase the number of Eritrean and Sudanese refugees coming from Israel, though talks with the UNHCR continue.
Some Israelis accused him of caving to left-wing pressure and betraying the residents of south Tel Aviv, a poor part of the city which has attracted the largest migrant community, changing its ethnic makeup and enraging some of its inhabitants who want the migrants out.
In February, about 20,000 male migrants were handed notices that said they had two months or leave the country or risk facing prison time.
These migrants were offered US$3,500 (S$3,937.50) to relocate to an unnamed "third country" - widely reported to be Uganda or Rwanda - or return to their home country.
Israel's Supreme Court had blocked deportations meant to begin on Sunday.
Moves to expel African asylum seekers were largely popular with the right-wing government's base, which viewed them as economic migrants who had entered the country illegally in search of work.
But rights groups advocating on behalf of the migrants say that many of them fled abuse and war and that their expulsion, even to a different country in Africa, would endanger them further.
The Israeli government pushed back against critics, in particular those who labeled the deportation policy racist, noting that thousands of Ukrainian and Georgian migrants were deported a year ago without being offered the relocation payment that was being offered to migrants from Sudan and Eritrea.
But in a dramatic about-face just hours after the announcement, Netanyahu said in a Facebook post he was suspending the implementation of the agreement while he consults with his officials.
The committee that came up with the plan stated that it will come up with a "rehabilitation plan" for southern Tel Aviv.
"The agreement stipulates that for each migrant who leaves the country, we commit to give temporary residence status to another", Netanyahu said in a televised address after Israel announced the deal. Israel has granted asylum to fewer than one percent of those who have applied and has a years-long backlog of applicants. Cabinet minister Naftali Bennett, leader of the nationalist Jewish Home party, said the deal turned Israel into a "paradise for infiltrators".
Some pro-migrant groups had welcomed the decision.
"I was really surprised", said Mr Yonatan Jakubowicz, founding director of the Israeli Immigration Policy Centre.
Mr Jakubowicz, a supporter of the previous policy, said he hoped the agreement with the United Nations refugee agency would be a positive, but he said many Israelis were hoping to see more leave.