Trump had repeatedly defended his immigration crackdown, including forcibly separating migrant children from their parents after they crossed the border.
Homeland Security Secretary Kirstjen Nielsen, the president and other officials have repeatedly said the only way to end the practice is for Congress to pass new legislation, though both Democrats and some Republicans have said the president could reverse it by himself.
Trump has been trying to win over congressional support on immigration amid a crisis along the border involving the separation of immigrant children from their families.
But Senate Democratic leader Chuck Schumer of NY signaled that no such support would be coming, saying it's already in Trump's power to keep the families together.
After a downturn a year ago, since October, the number of migrants seeking to cross the southwest U.S. border from impoverished Guatemala, El Salvador and Honduras, as well as from Mexico, has surged.
The second-ranking Republican, John Cornyn of Texas, said they're proposing a "humane, safe and secure family facility" where parents and minor children could be detained together.
The former president concluded by saying "we have to do more than say 'this isn't who we are.' We have to prove it - through our policies, our laws, our actions, and our votes".
More than 2,300 children have been taken from parents since May 5 under the current policy.
Melania was joined by all four of her living predecessors - Michelle Obama, Laura Bush, Hillary Clinton, and Rosalyn Carter - in condemning the policy.
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Among the day's losers, the yuan weakened to 6.491 to the dollar in the offshore market, the lowest in five months. Beijing has mounted campaigns against Japanese and South Korean companies in the past after diplomatic disputes.
Trump had tweeted earlier on Wednesday that he was "working on something".
The president however made clear he was not easing up on his determination to shut down the border to illegal immigration, calling it a source of rampant crime and drugs.
"I was just walking over to the Oval Office and I said, 'You know, it doesn't feel right to have a picnic for Congress when we're working on - doing something very important, '" Trump said. Until now, Trump and White House officals have instead been pushing GOP lawmakers this week to pass legislation that deals with immigration reform.
Democrats welcomed Trump's apparent change of course but said he had only himself to blame.
But immigrant advocates say that's misleading because customs officers aren't allowing many to enter the U.S.so they can legally claim asylum, forcing them to try to find other ways in.
The announcement from the Michigan Civil Rights Department came on the same day The Associated Press reported that the Trump administration is running three "tender age" detainment facilities in Texas, where undocumented babies and toddlers are sent after being forcibly separated from their parents.
Perry was not at the meeting with Trump, but said he doubts the president's words will affect his position. "And they are going for the country extremely well", the president said.
Attorneys and advocates say that some children whose parents seek asylum are in fact being separated at ports of entry and that they're hard to track down.
The House is to vote later this week on two bills that address broader immigration issues to protect young immigrant "Dreamers" from deportation and fund Trump's border wall.
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