Washington (CNN) The Trump administration has decided to refer every person caught crossing the border illegally for federal prosecution, a policy that could result in the separation of far more parents from their children at the border.

The move would also mean that even if immigrants caught at the border illegally have valid asylum claims, they could still end up with federal criminal convictions on their record regardless of whether a judge eventually finds they have a right to live and stay in the US.

Homeland Security Secretary Kirstjen Nielsen officially enacted the policy on Friday, according to a Department of Homeland Security official speaking on condition of anonymity. It corresponds with a Department of Justice "zero-tolerance policy" for illegal border crossings, under which Attorney General Jeff Sessions has ordered federal prosecutors to pursue criminal charges against all referrals for illegally crossing the border, as possible.

Sessions announced the change and reiterated his agency's policy at an appearance in Arizona on Monday.

"So, if you cross the border unlawfully, even a first offense, we're going to prosecute you," Sessions told a gathering of the Association of State Criminal Investigative Agencies. "If you're smuggling a child, we're going to prosecute you, and that child will be separated from you, probably, as required by law. If you don't want your child to be separated, then don't bring them across the border illegally."