The federal judge’s ruling was clear: The Trump administration could not use an obscure wartime law from the 18th century to deport people without a hearing.

If any planes were already in the air, the judge said, they should turn back.

That did not happen. Instead, the Trump administration sent more than 200 migrants to El Salvador over the weekend, including alleged gang members, on three planes.

A New York Times review of the flight data showed that none of the planes in question landed in El Salvador before the judge’s order, and that one of them did not even leave American soil until after the judge’s written order was posted online.

During a Monday court hearing, a Justice Department lawyer argued that the White House had not defied the order by the judge, James E. Boasberg of the Federal District Court in Washington.

The lawyer, Abhishek Kambli, argued that the judge’s decision was not complete until it was codified in written form. And — crucial to the government’s explanation — the written version did not include the specific instruction to turn planes around.

Mr. Kambli also argued that while the third plane contained deportees, their cases were not covered by the judge’s order.