Both bills would increase border security, grant funding for the president's border wall, and offer some form of amnesty to DACA recipients.
On Wednesday, House Speaker Paul Ryan said Republicans were working "hand-in-glove" with the White House on the proposal, and White House adviser Stephen Miller expressed support for the bill in a private meeting with Republicans.
The interviewer had specifically asked whether Trump supported a conservative bill written by Representative Bob Goodlatte, Republican of Virginia, or "something more moderate", and asked whether he'd sign "either one".
A move by renegade Republican moderates to force votes on bipartisan bills that would likely pass with considerable Democratic support was short-circuited this week by Ryan and other GOP leaders who feared passage of those bills would anger conservative voters in an election year.
"If this is not the option, then there's nothing else", Rep. Mario Diaz-Balart, R-Fla., who helped negotiate the compromise bill, said Thursday.
DACA has let the immigrants live and work in the U.S.in renewable two-year increments, but does not give them permanent legal status.
Seventeen killed in nightclub stampede in Venezuela
Outside the club, several mismatched shoes, including a sandal with a puckered red lip decoration, lay on the sidewalk. Authorities say non-governmental groups inflate figures to create paranoia and tarnish Maduro's socialist government.
GOP aides said Trump's remark caught party leaders off-guard, and White House officials did not immediately respond to requests to clarify the president's comment.
The draft bill ends the Diversity Visa Program and scales back family-based immigration visas, while offering a path to citizenship to dreamers that is contingent on the provision of border wall funding.
"I'm watching 100 percent the president because nothing is going to happen without his approval", said Alex Nowrasteh, an immigration policy expert with the libertarian-leaning Cato Institute. "He would sign either the Goodlatte or the leadership bills", White House spokesman Raj Shah said in a statement. Axios initially tweeted the bill "prevents children from being separated from their parents at the border" but has since updated its article to more clearly state how the GOP bill addresses family separation.
Just Wednesday, Ryan told House Republicans that Trump was enthusiastic about their effort on immigration.
"Everything we've heard has been very negative, I don't even know if they have the votes to pass the bill on their side", Pelosi said.
About 2000 Children Separated From Parents While Illegally Crossing the US Border
What do we know about the children? Mr Sessions said having children would not shield border-crossing migrants from prosecution. Franklin Graham, son of late reverend Billy Graham and a staunch Trump supporter, said the separation policy was "disgraceful".
It's unclear whether the president supports the bill.
Her spokeswoman said that Mrs Trump believes "we need to be a country that follows all laws", but also one "that governs with heart".
The compromise bill would end the practice of separating families at the border and provide legal protections to so-called Dreamers, immigrants brought to the US illegally as children, including a pathway to citizenship for at least some of them. "But some of the members of the conference have insisted that they have the opportunity to vote on both bills so that's what happened".
The draft legislation, resulting from intense negotiations between moderates and conservatives, includes a path to citizenship for an estimated 1.8 million young immigrants in the country illegally. Without it - as members thought they might be for several hours Friday - any immigration bill doesn't stand much a chance of passing in the House.
Both the conservative and compromise bills would provide money for Trump's long-sought border wall with Mexico.
Later Thursday, the White House vehemently defended its policy, even insisting that enforcing the law is "very biblical".
Taylor Swift's 7 Stylish Looks to Follow
On the 1989 tour, she was constantly donning the skater skirt and jazzing it up with an assortment of crop tops and sports coats. She attended her first Academy of Country Music Awards just five months before her first album was released, that was in 2006.