Title 42, a pandemic-era policy that allowed the U.S. to expedite deportations due to the COVID-19 pandemic, will not expire on Monday.
Arizona and Louisiana led 24 states in challenging the plan to end the restrictions.
A federal judge granted a preliminary injunction in the case on Friday.
A number of Republicans, and some Democrats, had called on the Biden administration to push back the elimination of Title 42. The Biden administration still pushed ahead.
In anticipation of Title 42's end, the Department of Homeland Security had deployed additional resources to the border to handle a potential influx of migrants seeking to enter the U.S.
Migrants have been expelled more than 1.9 million times since March 2020 under federal Title 42 authority.