Four months after the Trump administration deported Artemis Ghasemzadeh, a 27-year-old Iranian Christian convert, to Panama before she could seek asylum for fear of religious persecution, she is still living in limbo.

A 90-day humanitarian visa granted by the Panamanian government will run out in two weeks. Every day, she says, she wonders which country will provide her permanent refuge. Iran considers converting from Islam to any other religion a crime punishable by death.

On Tuesday, new U.S. legislation inspired by Ms. Ghasemzadeh will be introduced in Congress by Representative Yassamin Ansari, an Iranian-American Democratic lawmaker from Arizona. Called the Artemis Act, the bill seeks to prohibit the expedited removal of individuals fleeing countries that the State Department says persecute religious minorities — and ensure they have the chance to claim asylum in a U.S. immigration court.

Though Ms. Ansari says she expects widespread support from Democrats and has reached out to Republicans in hopes of generating bipartisan support, experts acknowledge that the bill has little chance of passing given that Republicans hold the majority of votes in the chamber.

It takes at least two countries to make a deportation happen: one to send deportees and one to receive them. Typically, the receiving country agrees to take back its own citizens, but the Trump administration is developing other options.

The U.S. has sent hundreds of deportees, most of whom appear to be Venezuelans, to El Salvador, where they are being held in a maximum-security prison notorious for its brutality. The U.S. has sent migrants from Asia, the Middle East and Africa to Panama and Costa Rica, including families with young children.

The Trump administration is also in early talks with the Rwandan government to send deportees to the central African country, and this month the U.S. made plans to send Laotian, Vietnamese and Filipino migrants to Libya before backing down in the face of a court order. (Representatives of Libya’s warring governments have since denied making any agreement to accept deportees from the United States.)

The expansion of the administration’s third-country deportation program appears to have two aims in the service of its overarching goal to remove millions of immigrants from the United States, including both undocumented immigrants and those who have legal status but are viewed as undesirable by the administration.

The first seems largely tactical: It creates a process to remove migrants whose countries of origin don’t want them back. Venezuela, for example, only sporadically accepts deportation flights from the United States.

The Trump administration is trying to deport a group of eight migrants to South Sudan, a country on the brink of civil war.

The men, who are from countries including Vietnam, Cuba and Mexico, are currently believed to be held at an American military base in the East African nation of Djibouti, after a federal judge ordered the administration not to turn them over to the government of South Sudan.

U.S. immigration law does, under some circumstances, allow people to be sent to countries that are not their own. But this has been rare under past administrations.

The Trump administration is attempting to do something more expansive: potentially sending large groups of people to dangerous places like South Sudan, Libya or a maximum-security prison in El Salvador, with little or no due process, even if their countries of origin are willing to take them back.

A federal court ordered the Trump administration on Tuesday to maintain custody of migrants on a deportation flight that immigrants’ lawyers said was headed to South Sudan, a transfer the judge said appeared to violate an injunction he issued in April.

“I am not going to order that the plane turn around,” said the judge, Brian E. Murphy of the Federal District Court in Boston. Instead, he said, any migrants in Department of Homeland Security custody must not leave U.S. control once the plane landed, at least until a hearing Wednesday to determine whether they had received adequate due process.

The order capped a tumultuous hearing hastily called by the judge, during which Trump officials said they could not say where the flight was or where it was going.

Judge Murphy repeatedly expressed concerns that the administration had violated his order not to deport immigrants to countries where they are not from and may face danger without giving them enough time to challenge their removal. And he warned that officials involved in the deportations who were aware of his order, including potentially the pilots of the plane, could face criminal sanctions. “Based on what I have been told,” he said, “this seems like it may be contempt.”

A mistake had been made. That much was clear.

The Trump administration had deported a Maryland man named Kilmar Armando Abrego Garcia to a prison in El Salvador, even though a judge had issued a ruling expressly prohibiting that from happening.

But when the news reached the Department of Homeland Security, it set off a dayslong scramble and clashes among officials in three different agencies over how to deal with what everyone knew had been an error. As it became clear that keeping it quiet was not an option, D.H.S. officials floated a series of ideas to control the story that raised alarms among Justice Department lawyers on the case.

In the days before the government’s error became public, D.H.S. officials discussed trying to portray Mr. Abrego Garcia as a “leader” of the violent street gang MS-13, even though they could find no evidence to support the claim. They considered ways to nullify the original order that barred his deportation to El Salvador. They sought to downplay the danger he might face in one of that country’s most notorious prisons.

And in the end, a senior Justice Department lawyer, Erez Reuveni, who counseled bringing Mr. Abrego Garcia back to the United States, was fired for what Attorney General Pam Bondi said was a failure to “zealously advocate on behalf of the United States.”