The plan had targeted some 42,000 migrants of Eritrean and Sudanese origin now living in Israel and denied refugee status or asylum.
A number of migrant rights groups petitioned the Supreme Court to block any such policy.
"The Israeli government's attempts to negotiate with Uganda or Rwanda over receiving deported asylum seekers had failed".
"At this stage, the possibility of removal to a third country is no longer relevant", the advisers said in a statement.
The government originally announced a plan under which it would present migrants with $3,500 and the opportunity to leave on their own accord, or face indefinite imprisonment with eventual forced expulsion.
A few hours later, Prime Minister Benjamin Netanyahu said on his Twitter account that he instructed Internal Minister Aryeh Deri to "prepare for an immediate opening of detention facilities for the infiltrators".
In early April, Netanyahu announced that he had canceled the newly announced agreement, which stipulated granting temporary residence to half of the African migrants in Israel with the relocation of the rest to Western countries.
Israel's highest judicial authority had ordered their release because of the government's inability to conclude an agreement with third-party host countries.
In his letter sent Monday, the politicians noted that they "were dismayed that the Treaty was suspended, then cancelled, depriving citizens of Sudan and Eritrea asylum-seekers in limbo without a clear plan of action".
Security along the once porous border has since been greatly tightened.
Official figures released by the Interior Ministry show Israel has some 42,000 African migrants, many of whom live in the impoverished neighborhoods of southern Tel Aviv.
The deportation plan, which offered each migrant $3,500 and a plane ticket to third-party countries, was furiously attacked by critics in Israel and overseas as a violation of worldwide law which prohibits involuntary repatriation in cases where deportees would be vulnerable to persecution. The deal stipulated that they would be jailed if they fail to leave the country.