The Africans started moving toward Israel in 2005, after neighboring Egypt violently quashed a refugee demonstration and word spread of safety and job opportunities in Israel.
Israel says it has reached a deal with the United Nations refugee agency to cancel the plan to deport thousands of African refugees. But the others would stay in Israel.
The fate of some 37,000 Africans in Israel has posed a moral dilemma for a state founded as a haven for Jews from persecution and a national home.
Moves to expel African asylum-seekers were largely popular with the right-wing government's base, which views them as economic migrants who entered the country illegally in search of work.
Speaking at a news conference with Israeli prime minister Benjamin Netanyahu, Israeli interior minister Arye Dery said that following tough negotiations with the UNHCR, Israel had agreed to resettle one asylum seeker in a Western country for every asylum seeker awarded temporary residency status in Israel.
A UNHCR spokesperson confirmed that an agreement had been reached, but gave no details.
In a Facebook post, Netanyahu says he will discuss the deal with Israeli residents of south Tel Aviv on Tuesday.
"I've chose to suspend implementation of this accord and to rethink the terms of the accord", Netanyahu wrote on his Facebook page, saying his move was in response to criticism of the deal.
In shake-up, Trump names Texas doc Ronny Jackson to lead Veterans Affairs
He set up a data-tracking center at headquarters in an effort to intervene before problems became crises . Trump even joked previous year that his signature phrase, "you're fired" would never be used with Shulkin.
Netanyahu said the U.N. High Commissioner for Refugees had agreed to organize and fund the new plan that would take five years to implement.
The statement on Monday said the new plan meant there was no longer a need to send migrants to unnamed third countries.
His calls were soon echoed by members of Netanyahu's own Likud party.
Israel considers the vast majority of the almost 40,000 migrants to be job seekers and has said it has no legal obligation to keep them.
Instead, it would see a minimum of 16,250 migrants resettled in Western nations including Canada, Germany and Italy.
Canada has an arrangement with Israeli authorities to suspend the deportation of individuals who have private sponsorship applications with Canada until they are processed, said Hursh Jaswal, spokesman for Canada's immigration minister. Both countries have denied having any deal in place with Israel.
The U.N.'s refugee agency had urged Israel to reconsider its original plan, saying migrants who have relocated to sub-Saharan Africa in the past few years were unsafe and ended up on the perilous migrant trail to Europe, some suffering abuse, torture and even dying on the way.
The optics of black asylum seekers accusing the country of racism has turned into a public relations liability for Israel, and groups of Israeli doctors, academics, poets, Holocaust survivors, rabbis and pilots have all appealed to halt the plan. Tens of thousands crossed the porous desert border before Israel completed a barrier in 2012 that stopped the influx.