"To those who wish to challenge the Trump Administration's commitment to public safety, national security, and the rule of law, I warn you: illegally entering this country will not be rewarded, but will instead be met with the full prosecutorial powers of the Department of Justice", he said.
The Republican-controlled U.S. Congress is also considering legislation to address the issue. "Go for it! WIN!"
An earlier report from Fox News Channel said the Trump administration was considering an executive order that would allow immigrant families who cross the border illegally to stay together longer than is now permitted.
"Congress and the courts created this problem, and Congress alone can fix it", Nielsen said during a White House press briefing on Monday.
The administration says children who have already been separated from their guardians will not be immediately reunited with their families.
May said Wednesday that images of children in cages were "deeply disturbing". "But we also don't want families to be locked up in internment centers in America".
The decree does not mandate separation of parents and children, however.
"I'd love to see immigration reform, we've been talking about it for a long time - there's a bipartisan bill filed in the U.S. Congress, so if he's so concerned he can take up the bill", Walsh added.
House Speaker Paul Ryan said the House will vote Thursday on legislation which keeps families together when immigrants are prosecuted at the border. "Clearly the president is hearing the uproar from our communities", said Rep. Pete Aguilar, D-Calif. The Republicans want security and insist on security for our country and we will have that. They don't care about crime and want illegal immigrants, no matter how bad they may be, to pour into and infest our Country, like MS-13.
But others pushed back on the idea that Homeland Security had led the rollback.