The March deportation flights saw more than 200 Venezuelans accused by the White House of being gang members deported to a jail in El Salvador.
During a 15 March hearing, Judge Boasberg imposed a temporary restraining order on the use of the wartime law and a 14-day halt to deportations covered by the proclamation.
After lawyers told him that the planes had already departed, he issued a verbal order for the flights to be turned around to the US.
The White House denied violating the court ruling.
US press secretary Karoline Leavitt said: "The administration did not 'refuse to comply' with a court order.
"The order, which had no lawful basis, was issued after terrorist TdA [Tren de Aragua] aliens had already been removed from US territory."
After two deportation flights continued to El Salvador despite his order that they be turned around, Judge Boasberg convened a hearing to discuss "possible defiance" of his ruling by the Trump administration.
In response, Trump took to TruthSocial to call Boasberg a "troublemaker and agitator" and call for his impeachment.
El Salvador has agreed to take in the deportees in exchange for $6m (£4.6m).
Earlier this week, Trump met with El Salvdador's President, Nayib Bukele, at the White House, and expressed an interest in sending more deportation flights to El Salvador.