First Lady Melania Trump, herself an immigrant, made a rare foray into policy matters, with a statement that the US must be a country that “governs with heart”.

Kirstjen Nielsen, the US Homeland Security secretary, took to Twitter to clarify the administration’s handling of undocumented immigrant children.

“We do not have a policy of separating families at the border. Period,” Nielsen said in one tweet, a statement that contradicts the president.

Trump has acknowledged the policy exists, but has refused to accept responsibility for it, instead pinning the blame on Democrats.

Several prominent Democrats, meanwhile, spent Father’s Day crisscrossing the Rio Grande Valley in Texas to meet with US border authorities and tour detention centres for apprehended children, including a former Walmart store that’s been converted into a shelter for nearly 1,500 immigrant boys.

A delegation to McAllen, Texas, was led by senators Jeff Merkley of Oregon and Chris Van Hollen of Maryland. Merkley hasn’t ruled out running for president in 2020, while Van Hollen is in charge of Senate Democrats’ 2018 campaign committee.

“What the president has discovered is this policy, which he put in place six weeks ago, is creating an uproar among the American people,” Van Hollen said.

“This is something that transcends politics. This is about moms and dads imagining their children being taken from them.”

Julian Castro, the former San Antonio mayor who served as housing and urban development secretary in the Obama administration, joined protesters at a border patrol processing centre in McAllen, where temperatures hit 36C at mid-afternoon.

“It amounts, essentially, to state-sponsored child abuse that is traumatising young children by taking them away from their parents, not letting them know when they’re going to see their parents again, keeping them in conditions that we wouldn’t want any of our children in,” Castro said. He, too, is considered a potential 2020 presidential contender.

Trump administration officials say the policy is intended to deter undocumented immigrants from making the trek to the US border with their children. But the president has repeatedly blamed Democrats, citing an unspecified law that he says requires children to be taken from parents who cross the border illegally.

White House officials are unable to cite any part of US law that dictates the separations, which were initiated in April, after US attorney general Jeff Sessions announced “zero tolerance” for unlawful border crossings.

Adults apprehended after crossing the border outside an official port of entry are to be arrested and prosecuted under Sessions’ decree, which leads to their children being removed.

Previously, border authorities often issued notices to appear in court to families apprehended crossing the border who claimed asylum, and then released them. Trump has derided that practice as “catch and release”, arguing that many of the immigrants never appear for court proceedings.

Republicans in the US Congress and the administration have pointed to a 1997 court settlement, regarding the treatment of immigrant children in federal custody, for legal justification of Sessions’ new policy.

The US separated about 1,995 children from their parents, and detained them, between mid-April and May 31, according to the Office of Refugee Resettlement at the Department of Health and Human Services, which is responsible for their care.

On Friday, Trump hinted in a tweet that the policy is intended as political leverage to force Democratic lawmakers to agree to changes to immigration law containing elements they oppose, including the construction of a wall on the US-Mexico border.

“The Democrats are forcing the break-up of families at the border with their horrible and cruel legislative agenda,” Trump said on Twitter.

“Any immigration bill must have full funding for the wall, end catch and release, Visa lottery and chain, and go to merit-based immigration. Go for it! WIN!”

Representative Mark Pocan, a Wisconsin Democrat, who joined Merkley and Van Hollen in Texas, said that he thinks Trump believes the policy is popular with his political base.

“While he thinks it’s something that works well for that 35% that still adore him, it doesn’t work well for their party in November,” he said. “I think they’re way miscalculating.”

Former first lady Laura Bush wrote, in an op-ed published by the Washington Post: “This zero-tolerance policy is cruel. It is immoral. And it breaks my heart.”

Democrats have refused to consent to the border wall or to the restrictions to legal immigration Trump has demanded, and instead hope to block family separations with standalone legislation.