The Trump administration asked the Supreme Court on Thursday to allow it to continue deporting immigrants to countries other than their own. Administration lawyers filed an emergency application after a lower federal court upheld a block on the program, finding that people could not be deported without a chance to contest their cases.

In the application, Solicitor General D. John Sauer urged the court to allow the deportations, calling the effort “an essential tool to remove certain aliens, including some of the worst criminal aliens.” Justice Ketanji Brown Jackson, who handles emergency applications, asked challengers to respond by Monday. The third-country deportations have been criticized because immigrants have been sent to countries with histories of human rights abuses.

Mr. Sauer argued that the court intervention halting the program had “created substantial logistical problems,” forcing cancellation of deportation flights. Earlier, James Percival at Homeland Security said more than 25,000 people had been deported under the program. The block by the U.S. Court of Appeals for the First Circuit sent officials scrambling, with immigrants removed from flights to Costa Rica, Honduras, and the Central African Republic.

In the emergency filing, Mr. Sauer said the administration had canceled a flight carrying 70 immigrants to three countries, requiring new diplomatic engagement.