WASHINGTON—U.S. District Judge Thomas Cullen on Tuesday threw out the Justice Department’s unusual lawsuit seeking to overturn a Maryland court rule that temporarily shields certain migrants from immediate deportation. In a 37-page opinion, Cullen—himself a Trump appointee—said the executive branch lacked legal standing to sue a co-equal branch and that federal judges are immune from such litigation. Allowing the case to proceed, he wrote, would invite a “constitutional free-for-all” and “offend the rule of law.” The Justice Department sued all 15 judges on Maryland’s federal bench in June after Chief Judge George L. Russell III issued a standing order halting removals until 4 p.m. on the second business day after a detainee files a habeas petition. Prosecutors argued the order undermined immigration enforcement, but Cullen said the government should challenge it through appeals in individual cases rather than by suing the judiciary en masse. The decision caps the administration’s latest clash with federal courts over its aggressive deportation policies, including the high-profile case of Salvadoran migrant Kilmar Abrego Garcia, whose removal was also paused under the Maryland order.