A complex and high-risk legal battle is playing out in federal courts over President Trump’s decision to use an 18th-century wartime law to deport Venezuelan migrants accused of gang membership.

In the latest development, a federal appeals court on Tuesday blocked Mr. Trump from using the powerful law, the Alien Enemies Act, to quickly deport the migrants. The court’s 2-1 ruling rejected the administration’s argument that they were part of an “invasion” of the United States by a foreign power.

The judges of the Fifth Circuit, considered one of the country’s most conservative appeals courts, said that their injunction applied only to the use of the Alien Enemies Act. They said it would not prevent the government from using other lawful means to remove foreign terrorists from the United States.

The case will now almost certainly head to the Supreme Court, where it would get a full hearing on the substantive question of whether Mr. Trump has used the act unlawfully. The Supreme Court has already issued orders limiting the government’s use of the law.