Venezuela announced Saturday that it had reached an agreement with the Trump administration to resume accepting deportation flights carrying migrants who were in the United States illegally, with the first one landing as soon as Sunday.

Part of Venezuela’s willingness to accept the flights appeared related to the plight of Venezuelan migrants whom the Trump administration recently sent to notorious prisons in El Salvador with little to no due process. In a statement on Saturday, a representative for the Venezuelan government said: “Migration isn’t a crime, and we will not rest until we achieve the return of all of those in need and rescue our brothers kidnapped in El Salvador.”

The White House did not respond to a request for comment Saturday, though one of the president’s close allies, Richard Grenell, said earlier this month that the Venezuelans had agreed to accept the flights.

Venezuela’s autocratic leader, Nicolás Maduro, suspended the deportation cooperation after the Trump administration revoked a Biden-era policy that allowed more oil to be produced in Venezuela and exported.

Since the suspension of the flights, Mr. Maduro has come under intense pressure from the Trump administration, which has been pressing various Latin American nations to take in more deportees. Secretary of State Marco Rubio said on social media that Venezuela would face new “severe and escalating” sanctions if it refused to accept its repatriated citizens.

Venezuelans have crossed the U.S.-Mexico border in record numbers in recent years, in response to the economic and social crisis consuming the nation, which Mr. Maduro blames on U.S. sanctions against his regime.

The agreement to resume the deportation flights comes after the Trump administration invoked an obscure wartime authority from 1798 called the Alien Enemies Act to deport Venezuelan migrants to El Salvador, whose strongman leader agreed to accept the migrants, putting them in prisons where conditions are so nightmarish that many experts say they constitute human rights abuses.

The use of the wartime authority has emerged as a flashpoint in a broader struggle between federal judges across the country, who have sought to curb many of Mr. Trump’s recent executive actions, and an administration that has come close to openly refusing to comply with judicial orders.

Last week, a federal judge in Washington issued a temporary order blocking the government from deporting any immigrants under the wartime authority, saying he did not believe the law offered grounds for the deportation flights.

The Trump administration had claimed that the Venezuelan migrants who had been sent to El Salvador were all criminal gang members, but the families of some of those men, as well as immigration lawyers, argued that this was not the case for all the deportees sent to El Salvadoran prisons. And the administration provided little detail as to whom the individuals it sent there actually were. There seemed to be little to no due process at play.

Mr. Trump has appeared captivated by the ability to send people to the prison complexes in El Salvador, threatening on Friday that those caught vandalizing Teslas could be banished there for 20 years.

The president and allies, including Elon Musk, went to war with the judge over his order restricting deportations, calling for the judge’s impeachment. The rapidly escalating spat caused Chief Justice John G. Roberts Jr. of the Supreme Court to weigh in with a rare statement, admonishing the calls for the judge’s impeachment. This spurred concerns of a constitutional crisis.

The Trump administration has continued to stonewall the judge’s questions about the deportations to El Salvador. “The government is not being terribly cooperative at this point,” said the judge, James E. Boasberg, at a hearing on Friday. “But I will get to the bottom of whether they violated my order and who was responsible.”

Saturday’s agreement could help Mr. Trump accelerate his plans for mass deportations, one of the central promises of his campaign. He has already enlisted military planes, sent people to third countries far from their homes and invoked the wartime law to achieve that goal. Arrests inside the country are up sharply relative to those in the Biden administration, but they are well below the levels Mr. Trump and his immigration advisers want.

The agreement to resume the deportation flights to Venezuela also comes a day after the Trump administration said that it would end a Biden-era program that allowed hundreds of thousands of people from Cuba, Haiti, Nicaragua and Venezuela to enter the United States lawfully and work for up to two years.

Zolan Kanno-Youngs and Annie Correal contributed reporting.