UNITED NATIONS - UN Secretary-General Antonio Guterres believes that children must not be traumatized by being separated from their parents, his spokesman, Stephane Dujarric, said on Monday.

His voice was just one of many raised in objection to a recently introduced US policy that separates children from parents who were arrested for illegally crossing from Mexico into the United States.

Some 2,000 children taken from parents have been put in detention centers in southwestern US states, US officials said.

"As a matter of principle, the secretary-general believes that refugees and migrants should always be treated with respect and dignity, and in accordance with existing international law," said Dujarric in a statement. "Family unity must be preserved."

The statement, read out by the spokesman at a regular press briefing, is seen by many as directed against the United States.

While the spokesman denied that the statement was directed specifically against the US policy, he admitted that the secretary-general was concerned about the situation along the Mexico-US border.

"What the secretary-general would like to see at all borders is to see people being treated with dignity and respect for their rights, that people claiming asylum be given proper hearings," Dujarric said. "This is not a position that he has specifically against the United States. This is a principled position that he has for the way refugees and migrants are treated the world over."

"We've all been following what's going on at the border and I think he is concerned as anyone else," said Dujarric.

UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein was more direct, saying he was deeply concerned about the US policies that "punish children for their parents' actions."

The Geneva-based UN official cited the American Association of Pediatrics' earlier comments calling the US approach a cruel practice of "government-sanctioned child abuse" which may cause "irreparable harm" with "lifelong consequences."

"The thought that any state would seek to deter parents by inflicting such abuse on children is unconscionable," said Zeid.

He called on the United States to immediately end the practice of forcible separation of these children, and encouraged the government to ratify the Convention on the Rights of the Child.

Measures should be taken to "ensure that the fundamental rights of all children, whatever their administrative status, will be at the center of all domestic laws and policies," he said.

US President Donald Trump continued to blame Democrats in Congress for their inaction over the arrests of parents and separate detention of their children.

On Monday, he repeated in tweets his accusation.

He said in one tweet: "It is the Democrats' fault for being weak and ineffective with Boarder Security and Crime. Tell them to start thinking about the people devastated by Crime coming from illegal immigration. Change the laws!"

He misspelled "border."

In another tweet the US president said: "Democrats can fix their forced family breakup at the Border by working with Republicans on new legislation, for a change! This is why we need more Republicans elected in November. Democrats are good at only three things, High Taxes, High Crime and Obstruction. Sad!"

However, various media outlets in the United States have "fact checked" his allegations, refuting them, with some going beyond merely calling them "untruths" to actually call them "lies," saying it is only his administration's policy that has caused the separation and detention of children.

But US Homeland Security Secretary Kirstjen Nielsen defended the president on Monday.

"We will not apologize for the job we do or for the job law enforcement does, for doing the job that the American people expect us to do," she said in a speech in New Orleans, Louisiana. "Illegal actions have and must have consequences. No more free passes, no more get-out-of-jail-free cards."

The spokeswoman for first lady Melania Trump said on Sunday that "Mrs. Trump hates to see children separated from their families and hopes both sides of the aisle (in Congress) can finally come together to achieve successful immigration reform."

As of Monday, three former first ladies have criticized the Trump policy.

Laura Bush, the wife of former Republican President George W. Bush, wrote on Twitter Sunday: "I appreciate the need to enforce and protect our international boundaries, but this zero-tolerance policy is cruel. It is immoral. And it breaks my heart."

Hillary Clinton, the wife of former President Bill Clinton, a Democrat, spoke out on Monday at a women's group in New York City, calling such family separation "an affront to our values."

"Jesus Christ said, 'Suffer the little children unto me' not 'let the little children suffer,'" she said in response to members of the administration citing biblical justification for her opposition to the policy.

Michelle Obama, the wife of former Democrat President Barack Obama, on Monday endorsed Laura Bush's Sunday tweet, saying, "Sometimes truth transcends party."