Mr Trump has sought to use the widespread outrage over the family separations to push through other immigration priorities that have stalled in Congress, such as funding for his long-promised wall along the Mexican border.
Earlier Tuesday, the president ramped up his attacks on illegal immigrants who "infest" America in a pair of tweets that, again, blamed Democrats. We do not want adults to bring children into this country unlawfully, either, placing those children at risk. He said Democrats should come to the table to come to an agreement on immigration legislation.
Denham has spearheaded an effort in the House for a vote on an immigration measure favored by moderates that would provide legal relief to "Dreamers" - young immigrants whose deportation was deferred under the Obama administration.
This means parents are sent for federal court proceedings and separated from their children, who can not be jailed under United States law.
But Trump himself put that bill in doubt. "I'm confident that if Washington turns down the political rhetoric and both parties are willing to work together, we can find a solution that keeps families together as we determine how to move forward".
Trump's Monday morning tweets come amid a growing backlash over his administration's "zero-tolerance" immigration policy.
As the United States protocol prohibits detaining children with their parents because the minors are not charged with a crime, family separation seems unavoidable.
The United Nations has slammed the separation practice as unconscionable, while Amnesty International blasted it as "nothing short of torture". "One of those values is that children should not be punished for the crimes of their parents", he added.
"For someone saying these children aren't hostages, it's tough to call them guests", said a top aide to Senate Republicans who was briefed on the President's demands. It also does not apply exclusively to children of illegal immigrants, which, attorney Gabriel Malor noted, means that many federal law enforcement agents are prohibited from separating children from their parents for any crime whatsoever, even non-immigration ones.
Since children can not be sent to the facilities where their parents are held, they are separated from them.
Heartbreaking cries of youngsters calling for their parents in tears can be heard on the tape, reportedly released by a whistleblower at one of the border camps. She says, 'I promise I'll behave, but please get me out of here.
Unaccompanied minors are also an issue for this administration, with the government confessing it had lost 1500 children placed in homes or foster families, prompting the viral hashtag #wherearethechildren?
The majority crossed the border without their parents.
The Trump administration separated 2,342 children from 2,206 parents along the US-Mexico border between May 5 and June 9.