AMNA NAWAZ: President Trump made carrying out the largest mass deportation in U.S. history a cornerstone of his 2024 campaign.

But there are reports he's unhappy with the pace of that effort so far.

GEOFF BENNETT: William Brangham reports now on a new controversial tactic to carry out the administration's crackdown on illegal migration.

WILLIAM BRANGHAM: This plane landed in San Jose, Costa Rica, last week, descending through a cloud of uncertainty.

On board were 135 people deported from the U.S. on a journey back to their home countries.

Or somewhere else.

None are Costa Rican citizens.

OMER BADILLA, Costa Rican Deputy Minister of Interior and Police (through translator): There are 65 children and 70 adults.

They are families.

Costa Rica is committed to voluntarily returning deportees to their country of origin in up to 30 days.

WILLIAM BRANGHAM: The group, hailing from as far away as China, Vietnam, and Ghana, were then bused to a rural holding facility paid for by the U.S. Costa Rica became the second Central American country after Panama to serve as a stopover for unauthorized migrants being removed from the U.S. by the Trump administration.

Panama accepted almost 300 deportees who were initially held under armed guard in this Panama City hotel.

Images of that group stuck inside, unable to leave, made headlines last week.

FRANK ABREGO, Minister of Security, Panama (through translator): We are providing them with all the necessary medical, food and comfort services, and we will continue to do so until the last one has left our country, which is what was agreed with the United States government.

WILLIAM BRANGHAM: More than half agreed to be returned to their home countries; 97 were sent to a facility in the Darien Gap, a treacherous point of passage at Panama's southern border with Colombia which is used by many migrants.

Susana Sabalza is a Panamanian migration lawyer representing a Taiwanese family, including a child under 5, who were sent to the Darien facility.

Do you have any understanding as to what the conditions are like in that facility?

SUSANA SABALZA, Panamanian Migration Lawyer (through translator): I haven't seen the conditions with my own eyes, but I have spoken to reporters who have, and they said the conditions weren't pleasant.

We have to keep in mind the children, who are the future of humanity.

If they're experiencing this type of trauma in a tropical refugee camp, I want to know that they are doing well and that they have good care.

DONALD TRUMP, President of the United States: If we could get them out of our country, we have other countries that would take them.

WILLIAM BRANGHAM: This new process, using Latin American countries as a temporary bridge for deportees, partly helps the administration because the U.S. doesn't always have diplomatic relationships with some of these migrants' countries of origin.

So by transferring them to other nations, it transfers the diplomatic labor of repatriation to them as well.

MUZAFFAR CHISHTI, Migration Policy Institute: This is a significant or even a mammoth departure from the practices of the past.

WILLIAM BRANGHAM: Muzaffar Chishti is a senior fellow at the Migration Policy Institute.

MUZAFFAR CHISHTI: The president has made no secret of the fact that he believes that he won this election using immigration as a calling card.

And that message has not been lost on every single agency head and Cabinet member of this administration.

They have decided that deportation machinery is now the number one paragraph of your job description.

What we have now seen is that we are enlisting nation-states in that enterprise.

WILLIAM BRANGHAM: Earlier this month, on his first international trip, Secretary of State Marco Rubio visited Central America, including stops in both Panama and Costa Rica.

Amid threats of U.S. tariffs, sanctions, and even retaking control of the Panama Canal, the countries agreed to serve as a stopover for deportees.

MARCO RUBIO, U.S. Secretary of State: We do a lot of other things with Panama that go beyond just the canal.

I mean, they have been a great partner on slowing down the rate of migration on the Darien -- coming across the Darien Gap and the like.

So, I think it was a good visit.

WILLIAM BRANGHAM: The Department of Homeland Security, which is central to the administration's deportation policy, did not respond to "News Hour"'s request for comment.

But Muzaffar Chishti says the process raises many questions, as does the administration's overall approach to migrants so far.

MUZAFFAR CHISHTI: There may be violations of U.S. law, especially with respect to people who have expressed fear of being returned.

The fact that they were not given access to counsel, the fact that they were not provided due process.

The second most important consideration is that this is being done with militaristic imagery.

I mean, it's not just optics.

It's optics with sound.

It is sort of an orchestra of military machinery at work that I think is deeply un-American.

WILLIAM BRANGHAM: In the meantime, lawyer Susana Sabalza is trying to figure out what comes next.

And she has a plea.

SUSANA SABALZA (through translator): We are asking our president of Panama and his counterpart in the United States to have a little compassion and that they give each case the opportunity to be reviewed before sending these families to the brink of death, because, at some point, this is going to be scrutinized by some international body.

And that's where we're going to see the consequences.

WILLIAM BRANGHAM: For the "PBS News Hour," I'm William Brangham.