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Under the terms of the agreement, announced on Thursday, the government must contact all individuals who had been turned away at borders as a result of the president's first executive order that came into force on January 27, and inform them they may seek re-entry.
It does not guarantee applicants will receive new visas nor does it award them compensation, but obliges the government to act in "good faith" when processing their paperwork.
The settlement also guarantees that those who reapply for their visas can do so with the help of the Department of Justice liaison for a three-month period.
The settlement brings an end to the case Darweesh v Trump, a nationwide class-action suit filed by two Iraqi men detained at New York's JFK airport because of the ban. They were represented by numerous rights groups including the American Civil Liberties Union (ACLU).
It was the first legal challenge to the original Muslim ban, and had previously succeeded in gaining an injunction on removing anyone from the US on the basis of the ban.
"Although the government dragged its feet for far too long, it has finally agreed to do the right thing and provide those excluded under the first Muslim ban with proper notice of their right to come to the United States," Lee Gelernt, an ACLU lawyer involved in the case, said. 
But the "legal fight against Muslim ban 2.0" would continue, he added, with the Supreme Court set to hold another hearing in October.