Acknowledging that the separation of migrant families along the southwest border may have compromised their right to seek asylum, the federal government has agreed to allow a second chance for up to 1,000 migrants who had been facing deportation.

In a settlement announced Thursday, lawyers for the government said that parents whose children were taken from them under the administration’s “zero-tolerance” border enforcement policy will again be able to make a case for asylum. They can also remain in the United States while their children pursue their own asylum cases.

Lawyers for immigrants challenging the thousands of family separations carried out along the border this spring had argued that losing their children had left parents too distraught to adequately make a case for asylum status. The asylum process can be grueling, often requiring lengthy interviews and documentary evidence. As a result, the lawyers said, many of the parents’ claims had been speedily denied.

“It’s an implicit recognition that they did wrong by these families in denying them meaningful access to the asylum system, and that wrong is now going to be made right,” said Simon Y. Sandoval-Moshenberg, legal director of the Immigrant Advocacy Program at the Legal Aid Justice Center, who represented the plaintiffs.