(CNN) A federal judge pressed government lawyers Thursday over whether the administration should be required to identify the thousands of children and parents who were separated at the southern border and released from government custody before June 26, 2018.

The exchange came during a hearing for Ms. L et al. vs. Immigration and Customs Enforcement et al., an ongoing family separation lawsuit.

"The fundamental premise of the lawsuit is that there's an unlawful separation practice initiated by this administration," said Judge Dana Sabraw.

"The June 26 date is completely arbitrary viewed in that light," he added, referring to the date when he issued a preliminary injunction blocking most family separations at the US-Mexico border and ordering that those already separated be reunited.

Scott Stewart, deputy assistant attorney general, argued that doing so would dramatically change the case and create a burdensome task for the government.

Read More