A US judge has ordered the government to pay the costs of reuniting immigrant families with their children after being separated at the US-Mexico border as part of President Donald Trump's “zero tolerance” policy.

The US government is currently in the process of reuniting nearly 2,000 children with their parents, although the Trump administration missed the deadline of July 10 Judge Dana Sabraw set in June to reunite nearly 100 of those immigrant children and their parents.

Immigrant parents have been told by immigration officials that they had to pay for their travel and DNA tests to verify family relationships before being reunited with their children. In response, the American Civil Liberties Union (ACLU) has filed a lawsuit against the government.

“It doesn't make any sense for any of the parents who have been separated to pay for anything,” said Sabraw at a hearing in San Diego on Friday.

At the hearing, Sarah Fabian, who is a lawyer for the government, said the US Department of Health and Human Services (HHS), which houses detained children, had limited resources.

Fabian called the judge's order “a huge ask on HHS.”

“The government will make it happen,” Sabraw responded.

The judge will also impose timelines on the government for reporting details about its effort to reunite the migrant families with their children.

Reunifications efforts have been slowed due to the need for DNA testing and criminal background checks on parents as well as the necessity of determining their fitness to care for their children, according to the government.

More than 2,000 separated children are currently in the US government's custody, according to the Department of Homeland Security, which claims that it is aware of their locations and is making an effort to reunite them with their families.

Broadcast pictures of young children held in enclosures behind chain-link fences have triggered angry protests across the US and elsewhere so far.