Lawyers for the man, Kilmer Abrego-Garcia, disputed US government allegations that he was a member of the MS-13 gang and demanded his immediate return to the United States.
The US government, however, said it did not have the legal authority to bring him back from El Salvador.
On March 15, Trump invoked the 1798 Alien Enemies Act to rapidly deport alleged members of the Venezuelan gang Tren de Aragua.
The administration said it sent two flights to El Salvador that day carrying deportees processed under the rarely used wartime statute and a third flight carrying people deported under other rules.
In Monday's filing, a US Immigration and Customs Enforcement official said Abrego-Garcia was wrongfully placed on the third flight despite a 2019 judgment granting him protection.
"Through administrative error, Abrego-Garcia was removed from the United States to El Salvador," ICE official Robert Cerna said in the court document.
"This was an oversight, and the removal was carried out in good faith based on the existence of a final order of removal and Abrego-Garcia's purported membership in MS-13."
The Trump administration invoked the 18th-century law to deport Venezuelans and Salvadoreans it alleges are violent gang members as part of its sweeping immigration crackdown.
Representatives for some deportees have denied any gang ties, and US courts have temporarily blocked use of the law while hearing legal challenges.
Abrego-Garcia's lawyers on March 28 called on the US District Court in Maryland to order his return to the US and halt US funding of his detention at the mega-prison in El Salvador, which they called a "notorious torture chamber".
"Although he has been accused of general 'gang affiliation,' the US government has never produced an iota of evidence to support this unfounded accusation," the complaint stated, adding that Abrego-Garcia is neither a member of nor affiliated with MS-13 or any other criminal or street gang.
Abrego-Garcia's wife later saw him in photos and video of him at the prison, identifying her husband through his distinctive tattoos and two scars on his head, the complaint stated.
In a court filing on Monday, the Trump administration said the US government did not have the authority to bring him back since he was no longer in US custody.
US Department of Homeland Security spokeswoman Tricia McLaughlin said "intelligence reports" showed Abrego-Garcia was a member of MS-13 and involved in human trafficking.
She provided no further details.
Abrego-Garcia's wife and five-year-old son are US citizens and reside in Maryland, the family's legal complaint said.
Abrego-Garcia was pulled over by ICE officers while driving on March 12 and handcuffed while his son, who has autism and is unable to communicate verbally, was in the backseat of the car, the complaint said.
The ICE official said the agency was aware of the earlier court order blocking Abrego-Garcia's removal.
He was not on the March 15 flight's initial manifest but was assigned to the flight as "an alternate" as other people were removed from the flight for various reasons, the official said.
with AP
