Speaking to Today, the president said children are in "jeopardy making that thousand-mile trek"

In a Friday interview, President Joe Biden had a stern warning for migrant families as his administration continues to grapple with the huge numbers of unaccompanied children arriving at the U.S.-Mexico border.

Biden, 78, the Today show's Craig Melvin that parents in South America and Mexico should not send their children here.

"Do not come here. Period," he said in a message to migrant parents. "They're in jeopardy making that thousand-mile trek."

Asked whether the situation at the southern border is a "crisis" — as it has been described by advocates as well as Biden's critics and, sometimes, by Biden himself — the president said the situation "is getting urgent action now."

"For example, a month ago, we had thousands of young kids in custody in places they shouldn't be, controlled by the Border Patrol. We have now cut that down dramatically."

Immigration at the southern border, and Biden's response, has been thrust into the national spot in recent months, as the U.S. government faces the latest in a pattern of increases in the number of unaccompanied migrant children crossing into the country.

Many have also criticized the detention-like conditions in which the children have been initially held during processing.

Rep. Alexandria Ocasio-Cortez called them "barbaric," though overburdened government officials have pleaded for patience and stressed they were trying to undertake a more compassionate approach than their predecessors.

As of April, as Melvin said on Today, more than 20,000 unaccompanied children were in the U.S. — an all-time record.

Under COVID-19 precautionary powers (and a policy enacted by former President Donald Trump), almost all migrants are being immediately expelled after entering the U.S. illegally. 

Children, however, are an exception — a reversal under Biden's administration after he campaigned with a more empathetic message on immigration.

More and more, because of changes in Mexico, migrant families are also being allowed to stay while their cases are processed, as are those people with what officials call "acute vulnerabilities."

Officials stopped sending unaccompanied minors back across the border in an effort to reverse what they say were Trump's "inhumane" and "ineffective" zero-tolerance policies, which expelled all migrants — including children — during the pandemic.

Biden began signing executive orders to reverse some of those policies hours after he took the oath of office in January.

In part because of the contrast between the two administrations and in part because of rampant rumors and misinformation outside the U.S., some of the new migrants believe Biden to be much more welcoming than Trump — though many restrictions are still in place

Speaking to Today, Biden lay the blame squarely at the feet of the Trump administration while conservatives have been assailing his choices.

"Hey look — here's what happened," Biden said. "The failure to have a real transition — the two departments that didn't give us access to virtually anything were the Immigration and the Defense Department. So we didn't fire out that they had fired a whole lot of people, that they were understaffed considerably."

Biden's Friday comments echoed remarks he gave in February, during an interview with ABC News: "I can say quite clearly: Don't come."

Speaking to Today, Biden said his administration was now communicating directly with would-be migrants in their home countries, urging them to apply for citizenship from their current homes, rather than by attempting to cross the border illegally.

"What we're doing now, is we're going back to those countries in question where most of the [immigration] is coming from and saying: 'Look. You can apply from your country. You don't have to make this trek,' " he said.

As advocates previously explained to PEOPLE, the majority of those coming to the U.S. illegally are attempting to escape dangerous situations.

"These children are fleeing situations of extraordinary danger and violence, otherwise they wouldn't be making the journey," said Jennifer Nagda, policy director at The Young Center for Immigrant Children's Rights, an advocacy group for immigrant children.

Homeland Security Secretary Alejandro Mayorkas said in March the Biden administration planned to invest $4 billion into Central America's Northern Triangle countries of El Salvador, Guatemala and Honduras in an effort to "address the root causes of migration."

In March, White House Press Secretary Jen Psaki addressed the conditions in which the migrant children were being held in the U.S., which have drawn the most scrutiny.

"It's not acceptable," she said. "But I think the challenge here is that there are only — there are not that many options. … We have a lot of critics, but many of them are not putting forward a lot of solutions."