He said his agency and the Department of Justice must figure out how to prosecute the parents without splitting them from their children, the Associated Press news agency reported.

The border official's decision paves the way for US immigration enforcement to revert largely to the approach under the Obama administration.

It means US border agents who stop undocumented adult migrants accompanied by children will hand them a court summons and allow them to go on their way, rather than hold them in a detention facility.

President Trump repeatedly lamented this "catch and release" policy before his administration began in April criminally prosecuting adult migrants and holding their children separately to deter border crossings.

On Monday, White House press secretary Sarah Sanders said the reality was that the US did not have the space to hold all the undocumented families coming across the US-Mexico border.

"We're not changing the policy," she told reporters. "We're simply out of resources."