US Attorney General Jeff Sessions announced the “zero tolerance” policy for immigrants last month.
The policy places adults trying to cross the border into custody, and places children in detention centres.
The adults, many who are seeking asylum, will face criminal prosecution for illegal entry.
Thousands of children have been detained and separated from their parents.
Outrage at the new policy has this week been compounded by the decision of the US to quit the UN Human Rights Council.
Mr Sessions announced the new policy would change the current law of charging first-time border crossers with a misdemeanour offence.
Now, those crossing face criminal prosecution – but as the children are too young to be charged with a crime, children and parents cannot be detained together.
This results in the children being taken away and deemed unaccompanied minors.
As unaccompanied minors, they are placed in custody of the Department of Health and Human Services and sent to a relative, foster home or a shelter.
Officials at these services are already almost out of space to house the children – and a Walmart in Texas has now been converted into a detention centre for the minors.
Officials have also announced plans to erect tent cities to hold hundreds more children in the scorching Texas desert.
Horrific reports have emerged of babies sleeping in cages under foil blankets.
In the past six weeks, approximately 2,000 children have been separated from their parents.
Some have been reunited, but many families are being kept apart for weeks or months.
Advocates of the separations are arguing that hundreds of children are taken from parents who commit various crimes across the US on a daily basis.
But activists against the policy say no other country in the world has a policy of separating families who intend to seek asylum.
Mexican Foreign Minister Luis Videgaray Caso said the separation of children from parents at the US border was “cruel and inhuman”, and clearly violated human rights.
President Trump has defended the policy and blamed Democrats for the problem of illegal immigration.
He wrote on Twitter: “Democrats are the problem.
“They don’t care about crime and want illegal immigrants, no matter how bad they may be, to pour into and infest our country, like MS-13 (a notorious Californian criminal gang of mostly Salvadorans, Hondurans, and Guatemalans).”
The president has faced fierce criticism over this tweet, with critics comparing the current state of affairs to Nazi Germany.
Attorney General Jeff Sessions responded to these accusations, saying: “Well, it’s a real exaggeration, of course.
“In Nazi Germany, they were keeping the Jews from leaving the country.”
Mr Trump said he wanted to “end the border crisis” by giving border officials the resources to “detain and remove illegal immigrant families altogether”.