When President Gustavo Petro of Colombia announced on social media on Sunday that he had turned back U.S. military planes carrying deportees, President Trump came down hard.

He threatened tariffs and penalties so extreme Mr. Petro was forced to back down. “They pushed until he had to bend,” Jorge Enrique Robledo, a former longtime Colombian senator, said in an interview.

Later that day, the White House and Mr. Petro’s government announced that Colombia would welcome all Colombian deportees, including those on military jets, and Mr. Trump declared victory.

The crisis riveted attention to the Trump administration’s deportation efforts; it also raised questions about the military planes deporting migrants, and why they angered Mr. Petro and other Latin American leaders.

No. Rarely, in recent times, if ever, defense officials say.

As part of the Trump administration’s crackdown on illegal migration, Mr. Trump signed an executive order last week authorizing the U.S. military to assist in securing the border.

The acting secretary of defense at the time, Robert Salesses, said in a statement last Wednesday that the Department of Defense would “provide military airlift” to support the Department of Homeland Security in the deportation of more than 5,000 “illegal aliens.”

Mr. Salesses said these were people being held by U.S. Customs and Border Protection at the southern border. He noted that the flights would take place after the State Department obtained “the requisite diplomatic clearances” and notified each country.

Symbolically, however, the military planes are emerging as crucial to the administration’s messaging around its efforts to crack down on migration.

On Friday, the White House press secretary, Karoline Leavitt, posted images of migrants filing onto a hulking, slate-gray C-17 Air Force plane, while shackled together. The caption read, “President Trump is sending a strong and clear message to the entire world: if you illegally enter the United States of America, you will face severe consequences.”

No, military planes have not replaced nonmilitary planes and so far represent a small fraction of the flights carrying out deportations under the administration: Only about six such flights have delivered deportees to other countries as of the end of Mr. Trump’s second week in office, according to a U.S. military spokesman.

During the same period, dozens of nonmilitary deportation flights left for countries around the hemisphere. The practice, schedule and the number of deportees on board has not changed under Mr. Trump, according to officials in Mexico, Guatemala, Colombia and Honduras.

But the commercial charters that resemble the planes used in everyday travel, which are operated by U.S. Customs and Immigration Enforcement, or I.C.E., have received less attention than the military planes.

Both the usual I.C.E. flights and the new military flights are overseen by the Department of Homeland Security. During both Mr. Biden’s term and Mr. Trump’s first term, the United States deported more than a million people, according to the Migration Policy Institute in Washington.

Only Guatemala and Ecuador were confirmed to have received U.S. military flights carrying deported migrants as of Thursday. Honduras and Peru are expected to receive military planes on Friday, a Defense Department official said.

While Colombia has agreed to receive such flights, no new military planes have been sent out since Mr. Petro turned back the two planes over the weekend, according to the U.S. military.

Mexico has said it has received only nonmilitary flights and has not said it will accept military planes.

Pete Hegseth, the new defense secretary under Mr. Trump, has promised to continue to use military planes. On his first official day on the job, Mr. Hegseth said, “This Pentagon snapped to last week.” Along with adding barriers and troops at the U.S. southern border, he said the military had also moved to “ensure mass deportations.”

He added: “That is something the Defense Department absolutely will continue to do.”

So far, the people returned since Mr. Trump took office, including those on the military planes, are primarily people apprehended under the Biden administration.

Those in the photographs posted by Mr. Trump’s press secretary were Guatemalan migrants apprehended after illegally crossing the border who had been held in detention since early January, according to Guatemalan migration officials.

Mr. Petro turned back two U.S. military planes bound for his country for a few reasons, according to his social media posts on Sunday morning and members of his government.

First, he was upset about how deportees on a nonmilitary flight had been treated while they were being transported to Brazil. (They were handcuffed and flown in a plane without air-conditioning that was forced to land in Manaus, in the Amazonian rainforest, after malfunctioning.)

Second, while Colombia’s government had authorized military flights — according to U.S. officials — Mr. Petro was caught off guard when he learned only a few hours beforehand that the military flights were scheduled to land in Bogotá, Colombia’s capital. (Officials in Guatemala have also said they are notified only shortly before military planes are scheduled to arrive.)

Mr. Petro also generally objected to putting deportees in handcuffs; officials said his government had an agreement with the Biden administration that permitted deportees to mostly travel without restraints.

Experts say handcuffs are sometimes used while a plane is in flight to prevent deportees from taking over the aircraft; in other cases, they are used when deportees are escorted on and off the aircraft.

Colombia never blocked nonmilitary deportation flights. In a post on Sunday, Mr. Petro said “on civilian planes, where they’re not treated like delinquents, we will welcome our compatriots.”

On Wednesday, Mr. Petro said online that his government was in dialogue with the Trump administration to establish a “protocol for dignified treatment” that would include allowing deportees to travel without handcuffs.

The U.S. military has a particular resonance in Latin America, experts say, especially for leftist leaders like Mr. Petro and President Luiz Inácio Lula da Silva of Brazil. They remember a time when the United States carried out covert American military operations in the region as part of an effort to subdue revolutionary movements in the name of defeating Communism.

The presence of the U.S. military can also threaten the notion of national sovereignty in countries like Mexico. President Claudia Sheinbaum of Mexico has said: “They can act within their borders. When it comes to Mexico, we defend our sovereignty and seek out dialogue so as to coordinate.”

However, regional officials are most concerned about how migrants are being treated on deportation flights, and have expressed particular concern over the use of handcuffs and chains.

Leaders in Latin America have also objected to the images that are being released of migrants in handcuffs and chains and to the way that Mr. Trump has described migrants, particularly deportees, whom on Monday he referred to as murderers, gang members and drug kingpins.

“We do not agree with calling a migrant ‘a delinquent,’” Ms. Sheinbaum said. “We defend our compatriots wherever they may be, but in particular in this moment in the United States.”

Since Mr. Trump took office, Brazil, Guatemala and Mexico have submitted complaints to the United States related to the treatment of migrants on deportation flights, according to officials in those countries. It was not immediately clear if in Guatemala the complaint was related to a deportee or deportees on military flights.

On Thursday, Colombian deportees said they had been handcuffed, shackled and chained around the waist for the duration of a flight to Bogotá on a nonmilitary plane; it was not immediately clear if the government there made an official complaint.

Reporting was contributed by Emiliano Rodríguez Mega and James Wagner from Mexico City; Jody García from Guatemala City; Federico Rios from Bogotá, Colombia; and Eric Schmitt from Washington.