Republicans are scrambling to draft a bill to address the growing outcry over the policy of separating migrant families at the US-Mexico border.
President Donald Trump told a group of House Republicans he would back any immigration bill they passed, a White House spokesman said.
The Republican-controlled Congress is under pressure to change the policy, following widespread condemnation.
But the president says it is necessary to stop illegal border crossings.
“We had a great meeting,” Mr Trump said after seeing Republican lawmakers on Tuesday.
It is unclear if any progress was made but White House spokesman Raj Shah said Mr Trump had told the group he would endorse their immigration legislation.
The president made clear that separating parents and children was “certainly not an attractive thing and does look bad”, Representative Tom Cole said.
Earlier on Tuesday Mr Trump said children had to be taken away if their parents were jailed for illegally crossing the US border.
“When you prosecute the parents for coming in illegally – which should happen – you have to take the children away,” he said.
US immigration officials say 2,342 children were separated from 2,206 parents between 5 May and 9 June amid a “zero-tolerance” crackdown on illegal immigration brought in by Attorney General Jeff Sessions.
What’s the latest reaction?
In an interview with Reuters news agency, Pope Francis said he supported recent statements by US Catholic bishops who called the policy “contrary to our Catholic values” and “immoral”.
Mexican Foreign Minister Luis Videgaray Caso said family separations were “cruel and inhuman”, and clearly violated human rights.
The US Chamber of Commerce and the Business Roundtable, two leading business groups, said the policy was “contrary to American values”.
Governors from at least eight US states – including two Republicans – have reversed their decision to send National Guard troops to the US-Mexico border.
A new Reuters/Ipsos opinion poll suggests that most Americans oppose the policy, with only 28% supporting it.
French far-right leader Marine Le Pen, who in the past has praised Mr Trump’s policy of curbing immigration, told French TV that she disagreed with splitting children from parents.
What is the policy?
Under the “zero-tolerance” approach unveiled in May, all undocumented border crossers are criminally charged and jailed.
Migrant children cannot be held with their parents, and are kept in separate facilities maintained by the Department of Health and Human Services.
Under previous US administrations, undocumented immigrants caught crossing the border for the first time tended to be issued with court summonses.
But the Trump administration points out that most of those migrants never showed up for court.
The White House has been disputing the terminology used to describe its crackdown.
It describes the holding centres where children have been pictured in metal chain-link enclosures with concrete floors as “shelters” instead of “cages”.
What are Trump and lawmakers doing?
The House of Representatives is preparing this week to vote on a moderate immigration bill.
The compromise would limit, but not ban outright, family separations. It would also offer an eventual path to citizenship for undocumented adult immigrants, known as Dreamers, who entered the US as children.
The Republican legislation would also provide $25bn (£19bn) in funding for border security, including Mr Trump’s planned US-Mexico wall.
House Republicans were reportedly working on a revised plan that would mean children would be detained for longer than is currently allowed but kept with their parents, the Associated Press reports.
Senate Majority Leader Mitch McConnell also said he “hoped to reach out to the Democrats” about crafting a bipartisan deal. However Democrats argue that no congressional action is required and the president can simply reverse his own policy.
More on US immigration
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