They also said the children were being well cared for and disputed reports of disorder and mistreatment at the border.
"While protecting our borders is important, we can and must do better as a government, and as a society, to find other ways to ensure that safety", he added.
Keilyn Enamorada Matute, from Honduras, with her 4-year old son, as they surrender themselves to Border Patrol agents after crossing the Rio Grande from Mexico to the United States, in McAllen, Texas.
"When all of our great-great-grandparents came to America they weren't 'animals, ' and these people aren't either", Senate Democratic Leader Chuck Schumer, D-N.Y., said, while Pelosi, D-Calif., said that "we are all God's children".
Trump caused controversy among some Democrats in May when he described MS-13 gang members as "animals".
And now Trump faces the consequences. Almost 60,000 children were placed in government-contracted shelters in the 2014 fiscal year. Even evangelical supporters like Franklin Graham said its policy was "disgraceful".
'Democrats and Republicans have spoken out against the practice.
Since that controversy erupted, Trump has repeatedly used the term proudly.
"No nation can have the policy that whole classes of people are immune from immigration law or enforcement", Miller told the Times.
The administration's critics are not buying that explanation.
Trump will meet with House Republicans next week to discuss the issue just days after his comments during an impromptu Fox News interview on the White House driveway almost derailed the planned House vote, according to a House GOP official who spoke on condition of anonymity to discuss the plans ahead of an official announcement.
White House press secretary Sarah Sanders cited the Bible to defend a border policy that has separated children from their parents.
Speaking on the CBS news show "Face the Nation", Sunday morning, the Republican also said the numbers of children who have been separated so far might exceed the almost 2,000 figure earlier reported. "It is immoral and we must call him out".
About 2,000 children were separated from their families over a six-week period ending in May. More than 11,000 immigrant children are being held in shelters by the Office of Refugee Resettlement, according to CNN.
The Trump administration's "zero tolerance" border security approach has seen thousands of adults criminally prosecuted for illegally entering the USA, meaning their children are separated from their guardians and classified as "unaccompanied minors".
With the crackdown in full swing, the detained parents are "in jail settings", the official said, awaiting adjudication and possible prosecution for crossing the border. The initiative yielded results and was soon expanded to more border sectors.
She called on Congress to simultaneously address Trump's border wall and the fate of the young immigrants left in limbo after the president rescinded the Deferred Action for Childhood Arrivals (DACA) program. Some of them insist a bill due to come before the House of Representatives next week would put an end to the separation of families.