A US federal judge has questioned why the Trump administration failed to obey his order halting the deportations of alleged Venezuelan gang members.

James Boasberg, the top federal judge in Washington DC, ordered deportation flights to be turned around on Saturday night.

White House officials argued in a court filing that they did not defy the ruling. The argued in part that because Boasberg’s order was made orally rather than in written form, it was not enforceable – and that the planes had already left the US by the time it was issued.

Boasberg has ordered the administration to give further details about the deportations by noon (16:00 GMT) on Tuesday.

He has requested further details about the timing of the order under which the deportations occurred, as well as details about the flights themselves.

During a hearing on Monday, Boasberg said he clearly ordered the government to turn the planes around.

“You’re saying that you felt you could disregard it because it wasn’t in a written order?” he asked Department of Justice lawyers.

In the same hearing on Monday, the judge said he would not make another ruling in the case until a hearing scheduled for Friday.

In the meantime, government lawyers said that the deportations had been paused. The Trump administration also asked in a court motion that Boasberg be removed from the case.

The dispute began over the weekend when a group of 238 alleged Venezuelan gang members, plus 23 alleged members of the international MS-13 gang, were sent from the US to a prison in El Salvador.

Announcing the move on Saturday, Trump accused the gang Tren de Aragua (TdA) of “perpetrating, attempting, and threatening an invasion or predatory incursion against the territory of the United States”.

He cited the Alien Enemies Act – legislation dating to 1798 that allows non-citizens to be deported in wartime. The act was last used during World War Two, when it was invoked to arrest and deport citizens of Axis countries.

Campaign groups have questioned Trump’s justification.

The act was used as the basis to deport 137 of the total of 261 people who were deported, the White House said on Monday. The basis on which the other deportees were removed from the US is unclear.

On Saturday, during the hearing that took place as several of the deportation flights were in the air, Boasberg ordered a 14-day pause.

After lawyers told the judge that planes with deportees already had taken off, he reportedly gave a verbal order for the flights to turn back “immediately”, although that directive was not included in a written ruling published shortly thereafter.

Nonetheless, a timeline of events reported by US media suggests the Trump administration had the opportunity to stop at least some of the deportations.

Under the US system of checks and balances, government agencies are expected to comply with a federal judge’s ruling.

But Trump’s Department of Justice argued, citing case law in a filing on Monday, that “an oral directive is not enforceable as an injunction”.

Administration officials also pointed out that the five named plaintiffs in the lawsuit that prompted the hearing were not among those deported, and also argued that once the flights left US airspace, the judge’s powers no longer applied.

White House press secretary Karoline Leavitt said: “The administration did not ‘refuse to comply’ with a court order.”

Neither the US government nor El Salvador has named those who have been deported, or provided details of their alleged criminality or gang membership.

Several relatives of men believed to be among the group told the New York Times that their loved ones did not have gang ties.

The White House, for its part, has insisted that authorities are “sure” that the detainees were gang members, based on intelligence.

Trump’s border tsar, Tom Homan, told reporters at the White House on Monday that Trump did “exactly the right thing”.

“The plane was already over international waters with a plane full of terrorists and significant public safety threats,” he said.

“We removed terrorists. That should be celebrated in this country.”

El Salvador has agreed to accept the deportees from the US.

The country’s president, Nayib Bukele, appeared to mock the judge’s ruling.

“Oopsie… Too late,” he posted on social media, along with a picture of a headline announcing the ruling and a ‘crying with laughter’ emoji.

His team also published footage of some of the detainees inside one of its mega-jails.

According to the White House, El Salvador’s government received $6m (£4.62m) to take the detainees, which Leavitt said “is pennies on the dollar” compared to the cost of holding inmates in US prisons.

The American Civil Liberties Union (ACLU), which brought the lawsuit leading to the judge’s order, questioned Trump’s use of the Alien Enemies Act, a sweeping wartime authority that allows fast-track deportations.

“I think we’re in very dangerous territory here in the United States with the invocation of this law,” said the ACLU’s Lee Gelernt.

The Alien Enemies Act only allowed deportations when the US was in a declared war with that foreign government, or was being invaded, Mr Gelernt said.

“A gang is not invading,” he told BBC News.

Making matters worse was the fact “the administration is saying nobody can review what they’re doing”, Mr Gelernt added.

Amnesty International USA said the deportations were “yet another example of the Trump administration’s racist targeting” of Venezuelans “based on sweeping claims of gang affiliation”.

Venezuela itself criticised Trump, saying he “unjustly criminalises Venezuelan migration”.

The latest deportations under Trump’s second term are part of the president’s long-running campaign against illegal immigration.

The two gangs targeted with the weekend deportations were declared “foreign terrorist organisations” by Trump after returning to the White House in January.

• 17:25 EDT: A first flight believed to be carrying deportees leaves Texas, according to data from tracking site Flightradar24. Take off happens while a hearing held by Judge Boasberg is paused. Earlier that afternoon, the White House said Trump was invoking the Alien Enemies Act
• 17:44 EDT: A second flight believed to be carrying deportees leaves Texas, according to Flightradar24
• 18:05 EDT: Boasberg’s hearing resumes
• 18:46 EDT: During the hearing, Boasberg verbally orders the government to turn around the two planes if they are carrying non-citizens, saying: “Any plane containing these folks – because it’s going to take off or it’s in the air – needs to be returned to the United States… This is something that you need to make sure is complied with immediately”
• 19:26 EDT: Boasberg issues his written ruling which includes a temporary restraining order on any further flights
• 19:36 EDT: A third flight believed to be carrying deportees leaves Texas, according to Flightradar24