LOS ANGELES — Many migrant families separated at the U.S.-Mexico border may have a second chance to claim asylum under a settlement agreement reached late Wednesday between the Trump administration and lawyers representing the parents.

The settlement, which is pending approval by a federal judge, would be major win for many of the parents of more than 2,500 migrant children who were forcibly separated by U.S. Customs and Border Protection and placed in separate detention facilities under the Trump administration's zero tolerance policy between April and June.

ACLU lawyer Lee Gelernt, who is representing many of the separated parents, said "the settlement will now finally give parents a meaningful opportunity to seek asylum with their children. As critically, it leaves open the possibility that some parents deported without their children can return to the United States."

NBC News previously reported that parents felt pressured to drop their asylum cases and be deported in order to see their children again.

Many deported parents say they were misled into thinking that leaving their children in the U.S. was the only way they would be reunited.

Under the settlement, parents and their children will be able to redo their interview with asylum officers to prove credible fear, the first bar immigrants must clear in order to pursue asylum.

For parents already deported, the government is willing to reconsider reopening their cases, but will not bring all deported parents back to the U.S.

Immigrants will also be able to have their lawyers present during the interview.

"The psychological state of the parent at the time of the initial interview" will be considered if there are inconsistencies in the information provided between the first and second interview, according to the settlement.

The Justice Department declined to comment. The Department of Homeland Security did not immediately respond to a request for comment.

Jacob Soboroff reported from Los Angeles. Julia Ainsley reported from Washington.