Republicans are scrambling to draft a bill to address the growing outcry over the policy of separating migrant families at the US-Mexico border.
US President Donald Trump told a group of House Republicans he would back any immigration bill they pass, a White House spokesman said.
The Republican-controlled Congress is under pressure to curb the policy after it sparked widespread condemnation.
But the president says it is necessary to curb illegal border crossing.
We had a great meeting, Mr Trump said after meeting Republican lawmakers on Capitol Hill on Tuesday night.
It was unclear if any progress was made, but White House spokesman Raj Shah said in a statement that Mr Trump told the group of lawmakers he would endorse their immigration legislation.
The president said in the meeting 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 from 5 May to 9 June amid a zero-tolerance crackdown on illegal immigration brought in by US Attorney General Jeff Sessions.
Mexican Foreign Minister Luis Videgaray Caso said on Tuesday that the family separations were cruel and inhuman, and clearly violated human rights.
The US Chamber of Commerce and the Business Roundtable, two of the top US business groups, called for the Trump administration to end the policy, calling it contrary to American values.
Governors from at least eight US states – including two Republicans – have said they will reverse their decision to send National Guard troops to the US-Mexico border over the separation policy.
A new Reuters/Ipsos national opinion poll suggests that most Americans oppose the policy, with only 28% of those interviewed supporting it.
Under the zero-tolerance crackdown that the Trump administration rolled out in May, all border crossers – including first-time offenders – are criminally charged and jailed.
Migrant children are not permitted to be incarcerated 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 immigration crackdown.
The Department of Homeland Security has framed it as an initiative rather than a policy.
It describes the holding centres where children have been pictured behind metal chain-link enclosures with concrete floors as shelters instead of cages.
The House of Representatives is preparing this week to vote on a moderate immigration bill.
The compromise measure would limit, but not outright ban 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 allow children to be detained for longer than is currently allowed but keeping them with their parents, the Associated Press reported.
Senate Majority Leader Mitch McConnell also said he hoped to reach out to the Democrats about crafting a bipartisan deal in the upper chamber. However Democrats argue that no congressional action is required and the president can simply reverse his own policy.
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