"You can't do it through an executive order," Mr. Trump told reporters last Friday.
The President's move came amid a growing firestorm of criticism in Congress from members of both parties in the Congress, stirred by stories of young children taken away from their parents.
"This must stop NOW," tweeted Rep. Justin Amash (R-MI), as he noted a story from his home state, where an 8-month old baby had been brought, after being taken from her parents.
"He can sign an executive order today," said Sen. Bill Nelson (D-FL), who was blocked on Tuesday from visiting a group of detained children at a federal facility in Homestead, Florida.
"This shameful chapter in American history lies with the President and his pen," Nelson said, arguing the President started these separations, and should halt them.
"We must stop the madness, and stop it now," said Rep. John Lewis (D-GA).
"America is weakened in the eyes of the world," added Rep. Hank Johnson (D-GA).
"This is a policy straight from the pit of hell," said Sen. Bob Casey (D-PA).
GOP leaders also made clear they wanted the Trump Administration to change course.
"As I said last week, we do not want children taken away from their parents," said House Speaker Paul Ryan, as he urged GOP lawmakers to unite behind a pair of immigration bills which are expected to be voted on Thursday.
But while the Speaker and other Republicans said provisions in those bills would fix the family separation matter - those plans would not advance through the Senate - making it unlikely that Congress could anything done on the family separation matter.
That left the President with just one option - an administrative reversal on something that he had fiercely stood behind the effort.
The change on illegal immigrant families came in early May, when Attorney General Jeff Sessions announced a "zero tolerance" policy dealing with those illegally coming over the southern border.
"Today we are here to send a message to the world: we are not going to let this country be overwhelmed," Sessions said in that May 7 speech.