“We have to remember that it is a choice to jail asylum seekers, and it is a choice that is at odds with international human rights norms,” said Heidi Altman, director of policy at the National Immigrant Justice Center.

Ms. Altman pointed to case management programs that have been used in the past to ensure that immigrants show up for court. Studies have shown that the programs are both cheaper than detention and have a proven track record of near universal court compliance.

To address the current crush of detained migrants, ICE officials are working urgently to both expand the current system and to purge it of anyone possible, according to two officials at the Department of Homeland Security who spoke under the condition of anonymity because they were not authorized to discuss internal operations. That effort involves scanning the records of the detained population to find anyone who is ready to be deported immediately, and to identify anyone who qualifies for humanitarian parole and can be released to make room for others.

Another idea, drafted in a memo from Mr. McAleenan in his new capacity as the acting homeland security secretary, would ask the Department of Justice’s Executive Office for Immigration Review to dedicate most or all of its resources toward processing the cases of detained immigrants — temporarily pausing the court proceedings of anyone who has already been released into the country. The memo has not yet been sent, according to the official who disclosed it.

Officials in Washington have also suggested to ICE field offices around the country that they begin to release immigrants who have been granted bond by judges but have not yet paid them — presumably because they cannot afford to — in order to make more room.