ABC News June 22, 2018

Hundreds of separated migrant families reunited

WATCH: Families hope to reunite with kids as debate over separation at the border continues

Hundreds of families that were separated at the U.S.-Mexico border after crossing illegally have been reunited, a source has told ABC News.

And in the wake of Donald Trump's signing of an executive order to halt families being torn apart, the Department of Homeland Security has ceased referring members of families to the Department of Justice to be prosecuted.

The Associated Press, citing a senior official in the Trump administration, reported earlier that about 500 of the more than 2,300 children separated from families have been reunited since May.

How many of the approximately 500 children were still detained with their families wasn't clear, and federal agencies were seeking a centralized process to reunite the remaining families, according to the AP.

(MORE: 'Zero-tolerance' approach not very effective, experts say) (MORE: 'Children are not poker chips': US mayors rally at border town against immigrant family separation policy) (MORE: Colbert on Melania's jacket: 'This is one message she did not steal from Michelle Obama')

Trump's so-called "zero-tolerance" approach has drawn criticism both from humanitarian groups and from law enforcement experts who've said it's not effective policy.

John Cohen, a former acting undersecretary at DHS and current ABC News consultant, said on Thursday that "zero-tolerance policies can quickly overwhelm the resources of the criminal justice system."

Patrick Semansky/AP
Darwin Micheal Mejia, left, and his mother Beata Mariana de Jesus Mejia-Mejia are escorted to a news conference after their reunion at Baltimore-Washington International Thurgood Marshall Airport on June 22, 2018, in Linthicum, Md.

Jails will overfill and officers will be removed from regular patrols to process detainees, and courts will "become inundated" with people who've committed minor crimes, Cohen added. Resources will be diverted from tackling more serious issues in communities.

Homeland Security Secretary Kirstjen Nielsen, at the 2018 Capital Hill National Security Forum on Thursday, said the border crisis is "a national security issue."

"Obviously," she added, "we are all focused in recent weeks on unaccompanied children and others who migrate across but unfortunately our loopholes encourage that behavior."

Meanwhile, the House of Representatives on Thursday rejected a conservative immigration proposal and delayed until next week a vote on a potential compromise in yet another setback for Republican leadership.