Sarah Rodriguez, an ICE spokeswoman, said the agency would try to find other relatives to place children with before sending them to the detention centers.

The operation is the latest phase of Mr. Trump’s ramped-up immigration enforcement. Shortly after he was inaugurated, he rescinded guidelines put in place by President Barack Obama that sought to limit arrests to those with serious criminal convictions. Apprehensions soared 38 percent during the first three months of his presidency compared with the same period last year.

The administration did not say how many parents had been arrested, and immigration advocates said that based on reports from lawyers, they did not think many had been.

But the effort could put hundreds, if not thousands, in jeopardy of arrest.

Unaccompanied children began to flood the southern United States border three years ago, when 68,541 were detained after fleeing violence and poverty in Central America. Since Mr. Trump took office, border crossings have plummeted to their lowest numbers in decades, possibly a result of his threats to arrest and deport greater numbers of undocumented immigrants.

Even so, from February through May, 5,445 children were detained after crossing the border unaccompanied by adult relatives, according to Customs and Border Protection, and a majority of those have wound up reunited with parents or other relatives.

A Salvadoran immigrant who gave only his first name, Jose, because he feared prosecution said in an interview Friday that he and his wife had come to the United States more than a decade ago, and that, as many young couples from their village did, they had left their toddler son, Henry, behind with relatives.

When Henry turned 13, gang members began to court him and threaten him for not joining them. In 2014, Jose wired money to a friend in El Salvador who said he knew of a coyote who could take Henry to the United States. “It’s impossible to do without help,” Jose said. “My son didn’t know the way, and it was dangerous.”