Washington (CNN) The Department of Health and Human Services does not have the capacity to care for the thousands of migrant children who could be separated from their families should the Trump administration reinstate the controversial policy, a senior agency official said Tuesday.

Senior administration officials told CNN that in the last four months or so, the President has been pushing Homeland Security Secretary Kirstjen Nielsen, who was forced to resign Sunday, to enforce a stricter and more widespread "zero tolerance" immigration policy -- not just the original policy started by former Attorney General Jeff Sessions and undone by the President once it was criticized.

Jonathan White, Commander of the Public Health Service Commissioned Corps, said in a Senate hearing said the administration would not be able to receive the number of children the program would require if implemented again, "nor do we have the capacity to serve them, nor is it possible to build a system that would prevent the mass traumatization of children."

White, who has been critical of family separations, told lawmakers Tuesday that he would "never support the use of family separation, the systematic traumatization of children as a tool of immigration policy," when asked if he would support a reinstatement of the "zero tolerance" policy that led to family separations last year.

"I would never support the use of family separation, the systematic traumatization of children as a tool of immigration policy, but it's not about what I support," White said.

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