About 500 of the more than 2,300 children separated from their families at the US border have been reunited since May, a senior Trump administration official has said.

Confusion has mounted along the US-Mexico border over the "zero-tolerance" policy that called for the prosecution of anyone caught entering the country illegally.

It was unclear how many of the roughly 500 children were still being detained with their families.

Federal agencies were working to set up a centralised reunification process for the remaining separated children and their families at the Port Isabel Detention Centre just north of border in Texas, said the official.

The US government was wrestling with the ramifications of President Donald Trump's move to stop separating families at the border and Congress again failing to take action on immigration amid outcry from all corners of the world, with the images and sounds of crying children dominating the news.

The Trump administration previously had not said whether any hundreds of children who were separated from their families had been reunited.

The official said many of reunited families were back together after a few days of separation. But other parents have said they do not know where their children are and were struggling to get answers.

Some mothers were deported without their children.

Meanwhile, there were signs that the administration was dialling back its "zero-tolerance" policy, for now.

The federal public defender's office for the region that covers cases from El Paso to San Antonio said on Thursday the US Attorney's Office would be dismissing cases in which parents were charged with illegally entering or re-entering the country and were subsequently separated from their children.

"Going forward, they will no longer bring criminal charges against a parent or parents entering the United States if they have their child with them," wrote Maureen Scott Franco, the federal public defender for the Western District of Texas, in an email shown to the AP.

In the Texas border city of McAllen, federal prosecutors unexpectedly did not pursue charges against 17 immigrants.

A federal prosecutor said "there was no prosecution sought" in light of Mr Trump's executive order ending the practice of separating families.

But the president showed no sign of softening.

The Trump administration began drawing up plans to house as many as 20,000 migrants on US military bases, though officials gave differing accounts as to whether those beds would be for children or for entire families.

The Justice Department also went to court in an attempt to overturn a decades-old settlement that limits to 20 days the amount of time migrant children can be locked up with their families.

"We have to be very, very strong on the border. If we don't do it, you will be inundated with people and you really won't have a country," Mr Trump said.

Thursday's uncertainty resulted from the abrupt ending on Wednesday of a White House-sanctioned practice of separating more than 2,300 children from their parents over the past several weeks.

After Mr Trump's executive order, a host of unanswered questions remained, including what will happen to the children already separated from their parents and where the government will house all the newly detained migrants, with the system already bursting at the seams.

Officials from the Defence Department and Health and Human Services (HHS) said the Pentagon has agreed to provide space on military bases to hold up to 20,000 people detained after illegally crossing the Mexican border.

It was unclear which bases would be used. But HHS has assessed four as prospective housing for children: Fort Bliss, Goodfellow Air Force Base and Dyess Air Force Base in Texas, and Little Rock Air Force Base in Arkansas.

The Justice Department asked a federal judge to change the rules regarding the detention of immigrant children, seeking permission to detain them for longer than the permitted 20 days in an effort to keep them together with their parents.

Meanwhile, the mayors of about 20 US cities gathered at a holding facility for immigrant children in the border city of El Paso. They accused Mr Trump of failing to address a crisis of his own making and called for the immediate reunification of immigrant children with their families.

"This is a humanitarian crisis," Seattle mayor Jenny Durkan said.

In Washington, the House killed a hard-right immigration bill on Thursday and Republican leaders delayed a planned vote on a compromise Republican package, with party members fiercely divided on the issue. Democrats oppose both measures.

The rejected bill would have curbed legal immigration and bolstered border security but would not have granted a pathway to citizenship to "Dreamers" who arrived in the country illegally as children.

The delayed vote was on a compromise bill between Republican moderates and conservatives that would offer Dreamers a pathway to citizenship and provide 25 billion dollars for Mr Trump's border wall, among other things.

Elsewhere, Democratic Governor Ralph Northam of Virginia ordered an investigation into claims by children at an immigration detention facility that they were beaten while handcuffed and locked up for long periods in solitary confinement, left nude and shivering in concrete cells.

First lady Melania Trump made a surprise visit to a McAllen detention centre that is housing some of the children. She told the children to "be kind and nice to each other".

She made waves while boarding the flight to McAllen in a green military-style jacket with the message "I really don't care, do u?" on the back.

Asked about it, her spokeswoman Stephanie Grisham said: "It's a jacket. There was no hidden message."

Mrs Trump was wearing a different jacket when the plane landed.