WASHINGTON — President Trump said Friday that next week he would close the southern border, or at least large sections of it, if Mexico does not halt illegal immigration into the United States, repeating a threat he has made before but never with a specific timetable.

In a series of tweets and later during appearances before reporters, Trump did not spell out exactly what a border closing would entail but said it could involve halting ‘‘all trade’’ between the two countries, a prospect that would have profound ramifications for the U.S. economy.

Trump blamed Mexico for a growing flow of ‘‘illegals’’ entering the United States and cited two large migrant caravans making their way toward the US border.

‘‘If they don’t stop them, we’re closing the border,’’ Trump said at an event in Florida. ‘‘We’ll close it. And we’ll keep it closed for a long time. I’m not playing games. Mexico has to stop it.’’

In another afternoon appearance, he said, ‘‘there’s a very good likelihood’’ that he’ll close the border next week.

Trump has threatened to close the border before but did not follow through.

Mexico’s new government, under President Andrés Manuel López Obrador, has actually been a willing partner with the Trump administration on migration issues.

Earlier this year, it allowed the implementation and expansion of a new US policy that forces asylum seekers to wait in Mexico as their cases are processed, in spite of criticism from human rights organizations.

Mexican immigration agents have also worked directly with US Customs and Border Protection to keep asylum seekers off US soil. At several major international bridges, Mexican agents now vet people before they reach the US side of the bridge.

Before he became president, López Obrador was a frequent critic of Trump, even publishing a book, titled ‘‘Listen, Trump,’’ which detailed his anger toward the White House. But he has tempered that critique to a previously unimaginable degree since taking office, in an effort to maintain a positive relationship with Trump.

On Friday, in the wake of Trump’s tweet about the possible border closure, López Obrador reiterated that approach.

‘‘We are going to help, to collaborate. We want to have a good relationship with the government of the United States. We are not going to argue about these issues,’’ he said at a news conference, in response to a question about Trump’s criticism of Mexican migration policies.

Trump’s comments came two days after the top US border official warned that the US immigration enforcement system along the nation’s southern boundary is at ‘‘the breaking point’’ and said authorities are having to release migrants into the country after background checks because of a crush of asylum-seeking families with children.

Kevin McAleenan, the commissioner of US Customs and Border Protection, said that for the first time in more than a decade, his agency is ‘‘reluctantly’’ performing direct releases of migrants, meaning they are not turned over to Immigration and Customs Enforcement, they are not detained, they are not given ankle bracelets to track their movements, and they are allowed to leave with just a notice to appear in court at a later date.

A move to close the border would come with numerous complications, including impeding US citizens seeking to reenter the country from Mexico.

El Paso, the Texas border city where the president held a rally in February calling for his wall with Mexico, is emerging as a flash point for the strained immigration system. Border Patrol agents in the city have begun holding migrant families in an area under a bridge, surrounded by fencing and razor wire.

Agents are apprehending about 570 migrants a day in the El Paso metropolitan area, up from about 100 a day five months ago. On some days last year, there were no apprehensions at all in the entire El Paso sector, which stretches across New Mexico and a swath of West Texas.

In another development, the former president of the American Academy of Pediatrics said that the death of a 7-year-old girl in Border Patrol custody last year could probably have been prevented with better medical treatment.

Dr. Colleen Kraft said an autopsy report released Friday on the death of Jakelin Caal Maquin shows the Guatemalan child contracted an infection with initially subtle symptoms before she began vomiting and experiencing a severe fever. Kraft said a trained professional would have caught possible signs like an elevated heartbeat or pulse.

Jakelin died Dec. 8, just over a day after she was apprehended by Border Patrol agents with her father.

At a rally in Grand Rapids, Mich., on Thursday night, Trump returned to the subject of the border, saying if Mexico does not stop migrants from trying to enter the United States, ‘‘we will close the damn border.’’

Material from the New York Times and the Associated Press was used in this report.