A Brazilian mother and 9-year-old son separated at the US-Mexico border were reunited after a federal judge in Chicago ordered the US government to release the child, saying their continued time apart "irreparably harms them both."

Judge Manish Shah mulled his decision for just a few hours before finding that Lidia Karine Souza can have custody of her son, Diogo, who has spent four weeks at a government-contracted shelter in Chicago. Shah ordered that the child be released yesterday, and hours later the mother and son were standing in front of a row of TV cameras smiling at each other.

Diogo wrapped his arm around his mom's waist and she wrapped hers around his shoulder.

The reunion occurred as the White House is under increasing pressure to bring families back together after a judge this week ordered federal officials to do so in 30 days for many parents and children.

More than 2,000 children remain separated from their parents, and critics say the government has no plan to reunite them.

White House spokeswoman Lindsay Walters told reporters on Air Force One that various federal agencies "are continuing to work through ensuring that remaining children are reunified with their parents."

When asked if the Health and Human Services Department -the agency that's in charge of reuniting families- will be able to comply with the 30-day deadline, she called on Congress to reform the nation's immigration system.

At the news conference at her lawyers' office in a Chicago high-rise building, Souza was asked if she had a message for President Donald Trump. Speaking through a Portuguese translator, she responded, "Don't do this to the children."

The mother, who has applied for asylum, was released from an immigrant detention facility in Texas on June 9 and is living with relatives outside Boston.

"Judge Shah has vindicated the rule of law and taken a definitive step to allow Lidia's son to finally be with her again. We are hopeful that this outcome will benefit other families facing similar circumstances," attorneys Jesse Bless and Britt Miller said in a written statement.

Shah, the son of immigrants from India, took just four hours before posting his written ruling after a hearing Thursday morning.

"Continued separation of ... (the) nine year-old child, and Souza," he wrote, "irreparably harms them both." In Washington, DC, police arrested nearly 600 people yesterday after hundreds of loudly chanting women demonstrated inside a Senate office building against Trump's immigration policy. Among those arrested was Rep. Pramila Jayapal, the Democrat from Washington state said on twitter.

Meanwhile, Melania Trump spent time with children at a complex in Phoenix where dozens of migrant children separated from their parents at the border are being held.

Souza's son spent four weeks at a government-contracted shelter in Chicago, much of it alone in a room, quarantined with chickenpox. He spent his ninth birthday on Monday without his mom.

The boy appeared relaxed at the news conference, speaking comfortably when asked questions by reporters. But he said the days after he was separated from his mom were difficult.

"I cried almost every day I wasn't with my mother," he said through a translator.

Even after Tuesday's ruling in California, Souza's attorneys nonetheless moved forward with an emergency hearing in their lawsuit against the Trump administration.

Shah wrote that he understood that volume of paperwork, filings and forms normally required before the government can release a child in its custody are intended to ensure the child's well-being.

But, he said, "the government's interests in completing certain procedures to be sure that (Souza's child) is placed in a safe environment and in managing the response to ongoing class litigation do not outweigh the family's interest in reuniting."

The fitness of the mother in this case isn't questioned, he said, so dragging out processing "only serves to interfere in the family's integrity with little to no benefit to the government's interests."

Souza had been allowed to phone her son for just 20 minutes per week. She has said he would beg her though tears to do everything in her power to get him back to her.

The 27-year-old woman searched for weeks to find Diogo after the two were separated at the border in late May. When she was released, she filled out nearly 40 pages of documents that US officials told her were required to regain custody.

Then they told her that the rules had changed and that she needed any family members living with her in the United States to be fingerprinted and still more documents.

Government attorney Craig Oswald told Shah that U.S. officials have been "raked over the coals ... before" for not being thorough about such background checks, which he said are meant to ensure a child's safety.

Souza was seeking safety by coming to the US, but it's not the safety she sought for herself and her son. This was not the American dream.

"This ... is a nightmare," she said in an interview with The Associated Press on Wednesday.

For days and weeks now, some of the hundreds of parents separated from their children at the Mexican border by the Trump administration have been battling one of the world's most complex immigration systems to find their youngsters and get them back.