But he added that he is scared that "millions of people are coming up, overtaking the country". In a speech Tuesday, he said congressional action was the way to resolve the issue. The language also leaves room to separate children from parents if it's best for the child's welfare.
Since early May, more than 2,000 children have been separated from their parents after crossing the U.S. -Mexico border illegally, as part of the administration's new immigration strategy, which prompted widespread outcry.
"We're going to keep families together but we still have to maintain toughness or our country will be overrun by people, by crime, by all of the things that we don't stand for and that we don't want", Trump said.
Pictures of dozens of children sleeping in fenced enclosures and audio of crying children sparked anger in the USA from groups ranging from clergy to influential business leaders, as well as condemnation from overseas, including Pope Francis.
"Migrant children should not be separated from their families, and both sides of the aisle can agree that we must quickly and permanently address this problem", Tillis said.
On Wednesday, Trump said the "zero tolerance" policy would remain in place.
When reporters shouted out questions, he briefly said that both Ivanka and Melanie felt "very strongly" about this, as did he. My wife feels very strongly about it. Instinctively combative and fond of chaos, Trump usually digs in on controversial policies, rather than backing down. "And they blame the White House for that".
The revised bill would also give Department of Homeland Security the authority to use $7 billion in border technology funding to pay for family detention centres, the person said.
Under the bill, children under age 18 would be kept with their families in residential centers during legal proceedings. But concurrently, organizers are already planning to take their message of support for separated families to Washington, D.C. on June 30, as well as via coordinated rallies across the country.
Under the administration's current policy, all unlawful crossings are referred for prosecution - a process that moves adults to the custody of the U.S. Marshals Service and sends many children to facilities run by the Department of Health and Human Services.
Joachim Low: 'Germany will not change game plan following Mexico loss'
The proof is in audio clips of his narration of the moment when Lozano placed a flawless kick to secure Mexico's early lead. Germany pressed in the second half but struggled to find the target. "If we go on like this, I'll be anxious ", he added.
"We are going to see what happens", Mr. Trump said. In Trump's new executive order, the defense secretary is instructed to take all available measures to provide to the Department of Homeland Security any existing facilities for the housing and care of "alien families" or to build them if necessary.
The Trump policy of separating children from parents crossing into the US, including those fleeing from violence, has been widely condemned including by Amnesty International.
Trump has made a tough stance on immigration central to his presidency.
One of the people said Nielsen, who had become the face of the administration's policy, had little faith that Congress would act to fix the separation issue and felt compelled to act.
He was also facing mounting pressure from within his own party, with some Republicans anxious there was going to be voter backlash in November if a resolution to the issue wasn't found.
Until Wednesday, Trump had held firm on the matter.
House Republican leaders are primarily still focused on upcoming votes on a pair of broader immigration bills.
When he got to immigration, the President said he was supportive of the House GOP efforts, but left some members unclear what he actually supported (the White House put out a statement after the meeting saying he supported the compromise bill).
Even if Republicans manage to pass one of the immigration bills through the House, it is all but certain to fizzle in the Senate, where Republicans are rallying behind a different approach. Previously, families who crossed the border were generally held together and brought through immigration court, where they faced civil penalties and subsequently could be deported.