Netanyahu said he would meet on Tuesday with residents of southern Tel Aviv, where many of the African migrants have settled, after they issued a statement condemning the new deal as "a shame for the state of Israel".
Several ministers also said they opposed the accord with the UNHCR of which they had not been informed before it had been announced by Netanyahu's office.
Netanyahu had said earlier that the new deal would see a minimum of 16,250 migrants resettled in Western nations including Canada, Germany and Italy.
"The agreement stipulates that for each migrant who leaves the country, we commit to give temporary residence status to another," he said in a televised address.
Germany and Italy, however, said they were unaware of any such resettlement deal for African migrants from Israel.
Israel announced Monday it had reached a deal with the UN refugee agency to cancel a controversial plan to deport African migrants and replace it with a new one that will see thousands sent to Western countries.
The deal meant thousands more of the primarily Sudanese and Eritrean migrants would remain in Israel at least temporarily.
It also put an end to the possibility that many would be forcibly deported to an unnamed African country, widely believed to be Uganda or Rwanda.
A minimum of 16,250 migrants would be resettled in Western nations including Canada, Germany and Italy under the agreement, Prime Minister Benjamin Netanyahu said at the time.
"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.
Netanyahu in January announced the implementation of a programme to remove migrants who entered illegally, giving them a choice between leaving voluntarily or facing indefinite imprisonment with eventual forced expulsion.
According to interior ministry figures, there are currently some 42,000 African migrants in Israel, half of them children, women or men with families, who are not facing immediate deportation.
They are mainly Sudanese and Eritrean.
As the migrants could face danger or imprisonment if returned to their homelands, Israel offered to relocate them to an unnamed African country, which deportees and aid workers said was Rwanda or Uganda.
The statement on Monday said the new plan meant there was no longer a need to send migrants to unnamed third countries.
The plans had drawn sharp criticism from the United Nations refugee agency as well as from some Israelis and rights activists.
The migrants' presence in Israel has become a political issue, with Netanyahu referring to them as "not refugees but illegal infiltrators".