Pompeo's statement did not refer to the current situation along the border with Mexico that has generated controversy as young children, including toddlers and babies, according to an Associated Press report, have been placed in shelters after being separated from their families who illegally crossed into the US.
On Tuesday, the Minister had expressed Mexico's "emphatic condemnation" of the U.S. border policy, calling it "cruel and inhumane".
The "zero-tolerance" policy has overwhelmed the federal government with caring for the new influx of children, who are often much younger than the teen immigrants who have typically been traveling alone to the U.S.
Videgaray highlighted the "particularly painful case" of a 10-year-old Mexican girl with Down syndrome who was taken away from her mother last week and is in a shelter in McAllen, Tex.
Mexico also has a complicated relationship with the hundreds of thousands of Central Americans trying to transit the country.
The family spent months seeking Mexican refugee status, a step taken by more and more Central Americans heading north, to allow them to avoid extortion or deportation while they gather resources to make the next move into the United States. "However, according to our constitutional principles and our convictions, we can not be indifferent before an act that clearly represents a violation of human rights and that puts into a vulnerable position minors, children, including those with disabilities".
The 10-year-old girl's case gained national attention after Donald Trump's former campaign manager Corey Lewandowski mocked her story on Fox News. A fourth, planned for Houston, would house up to 240 children in a warehouse previously used for people displaced by Hurricane Harvey, Mayor Sylvester Turner said.
Mexico on Wednesday demanded US authorities immediately reunite a girl with Down's syndrome and her brother with their parents.
Of some 1,995 cases registered by USA authorities, only around one percent of the children affected were Mexican, and most had already been repatriated, Videgaray said.
He said the Mexican government has been providing support since the policy was announced. Indeed some recent detainees are infants, taken from their mothers. All but seven of those have been repatriated.
Mexican authorities were working to achieve the reunification of all of the families involved.
Some 21 Mexican children had been identified as having been separated from their parents but most of the children affected are from Guatemala, El Salvador and Honduras.
President Donald Trump and administration officials have repeatedly said that federal law compels them to separate families, but Republican as well as Democratic lawmakers have pointed out that's simply not true.
Many families, like the Floreses, left Central America long before the zero tolerance policy - and while returning home is not an option, neither is separation.
On Tuesday, Trump once again tried to blame Democrats for the family separation crisis and took a swipe at Mexico as well. Border Protection said the mother is not being prosecuted, but rather is being held as a witness to alleged human smuggling.
While doctors and lawyers who have visited the shelters described them as clean and safe, they said the kids were acting out from the stress of not knowing where their parents were.
The family separation issue also triggered comments from Mexican presidential candidates.
Vanessa Bonilla also prepared to apply for US asylum, having traveled with her three young children from Honduras.
Some members of his party are demanding an end to it and the White House has said it is looking at emergency legislation meant to keep immigrant families together, tabled by Republican senator Ted Cruz, of Texas.
Videgaray, the Mexican foreign minister, said Central American officials would convene in Mexico in the coming days to formulate a further response to the Trump administration, with the goal of "ending this policy that violates the human rights of girls and boys, no matter their nationality". All have assailed what is widely viewed in Mexico as Trump's anti-Mexico and anti-immigrant posture.
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