More than a dozen states sued the Trump administration on Tuesday over its separation of migrant children and parents at the US-Mexico border, saying US President Donald Trump's order last week ending the breakups was illusory.

In a complaint filed with US District Court in Seattle, 17 states and the District of Columbia argued the administration's policy was unconstitutional in part because it was "motivated by animus and a desire to harm" immigrants arriving from Latin America.

"The new federal executive order does not bring back together the thousands of families that were torn apart by the federal government's policy, and it does not prevent families from being separated in the future," Illinois Attorney General Lisa Madigan, a Democrat, said in a statement on the lawsuit.

The family separations began because of the administration's two-month-old "zero tolerance" policy of seeking to prosecute all adults who cross the border illegally, including those traveling with children.

But Trump backtracked last Wednesday amid outrage spurred by images of children being held in cages.

In an executive order ending the family separations, Trump did not explain how his immigration policies could be adjusted to keep families intact and house them while their legal status is assessed.

Although the administration has said the zero tolerance policy remains in place, officials said on Monday that parents who crossed illegally with their children would not face prosecution for the time being, because the government was running short of space to house them.

Health and Human Services Secretary Alex Azar told a Senate hearing on Tuesday that most of the 2,000-plus children who had been separated from their parents could not be reunited with them until Congress passes new legislation.

A 1997 court settlement known as the Flores agreement set policy for the detention of minors in the custody of immigration officials, and a federal appeals court has interpreted it to allow immigration officials to detain families for only 20 days.

While that settlement is in place, Azar said the children could not be moved to be with their parents in detention.

"I cannot reunite them while the parents are in custody because the court order doesn't allow kids to be with their parents for more than 20 days," Azar said.

He called on Congress to fix the Flores agreement. Until it does so, he said, HHS will have to wait for families to go through immigration proceedings or be granted asylum before reuniting children with their parents.

- Reuters