The Director of Homeland Security did the same, saying it's Congress's job to change immigration law.
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An audio recording that appears to capture the heartbreaking voices of small Spanish-speaking children crying out for their parents at a U.S. immigration facility took center stage Monday in the growing uproar.
"Papa! Papa!" one child is heard weeping in the audio file that was first reported by the nonprofit ProPublica and later provide to The Associated Press.
Human rights attorney Jennifer Harbury said she received the tape from a whistleblower and told ProPublica it was recorded in the last week. She did not provide details about where exactly it was recorded.
The policy is drawing huge criticism from community activists and politicians, many of whom say separating children from their parents is not only inhumane, but anti-American.
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No one knows about the fight to keep a family together better than Francisca Lina. The 48-year-old mother of five has been taking sanctuary inside a Humboldt Park church for more than a year, since the day she was scheduled to be deported to Mexico.
As outcry against separation of children at border grows, Trump defends policy
Lina said she is willing to defy the law if it means not being permanently separated from her children, who are all U.S. citizens.
"I didn't do anything wrong, and I don't have a criminal record. I didn't want to take my daughters to that country, where there is a lot of violence," Lina said.
She can relate to the thousands of families being separated on the border. Since the Trump administration announced its zero tolerance policy of prosecuting all cases of illegal entry to the United States six weeks ago, nearly 2,000 children have been taken from their parents. They are being housed in old warehouses with metal fencing. The kids are given foil sheets as blankets.
"Separating a parent from their child, who is only trying to bring their child to a better tomorrow, is not who we are, not what we believe in," said Chicago Mayor Rahm Emanuel.
Emanuel joined many others - including former First Ladies Laura Bush, Michelle Obama, Hillary Clinton and Rosalynn Carter - in denouncing the Trump policy. But the president is not apologizing or backing down.
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"The U.S. will not be a migrant camp or a refugee holding facility," Trump said.
While it is his policy, Trump blames Democrats for the situation at the border.
"I think it is unfortunate that the president is twisting this," said U.S. Rep. Mike Quigley (D-Chicago).
Quigley said Democrats in Congress are likely to introduce an amendment to end the policy, but the party still holds a minority in the House and Senate. While some Republicans have publicly denounced the policy, Quigley said many more have remained silent. The ones who have spoken out are also not running for reelection.
U.S. Senator Tammy Duckworth (D-IL) also released a statement condemning the policy, saying, "Separating families to inflict trauma on children and parents seeking asylum in America is wrong, plain and simple. No one is forcing the Trump Administration's hand here. Donald Trump, Attorney General Sessions and Secretary Nielsen are making a conscious and completely unnecessary decision to rip children from their families under the guise of 'strong law enforcement' and lying to the American people about it. There is nothing strong about tearing families apart-it is inhumane, it is morally bankrupt and it goes against the values of this country."
The Associated Press contributed to this report.