President Trump blessed House Republicans’ compromise immigration bill “1,000 percent” Tuesday, giving political cover to conservatives looking to back the bill and creating momentum ahead of a showdown vote expected this week.

He said the legislation, which grants citizenship rights to illegal immigrant “Dreamers,” funds his border wall, limits the chain of family migration and ends the visa lottery, checks off all the boxes on his immediate immigration wish list.

Meeting with Republicans for an hour Tuesday evening, Mr. Trump told them he would welcome a fix to the family separation issue that has engulfed the immigration debate this week. But he made clear that any action would have to come from Congress, not from the administration.

His blessing clears up the mess he left Friday when he said he wouldn’t sign the bill. The White House later said he misunderstood the question, but his wavering left a number of conservatives fearful of voting for the bill only to have the president walk away from the legislation, leaving them on a political ledge.

“He says, ‘I am behind you 1,000 percent and I am not going to leave you out to dry,’ ” said Rep. Cathy McMorris Rodgers, Washington Republican and chairwoman of the House Republican Conference.

Whether that is good enough to win the votes of 218 Republicans — the number needed to approve the bill — is unclear.

“It’s going to be close,” said Rep. Carlos Curbelo, a Florida Republican who helped craft the compromise bill. “This is a very challenging issue, very controversial. All members are going to have to take some risks to make this happen.”

Rep. Mark Meadows, North Carolina Republican and head of the Freedom Caucus, said he is still weighing his vote, but the bill is a no-go for other conservatives.

“I think there are some who believe that it is amnesty, and they don’t want to vote for amnesty,” he said.

He also said some on the liberal side of the party wanted a more generous legalization for Dreamers.

“We represent very different districts,” he said. “The thing that motivates me to stay involved is I think the moderates negotiated in good faith — whether we get to 218 or not, I don’t know.”

Republican leaders released the official version of the bill Tuesday evening while Mr. Trump was meeting with them.

The bill would grant full legal status and a path to citizenship to people who qualify for the Obama-era Deferred Action for Childhood Arrivals program. The bill also would end the visa lottery and limit the types of family members who can be sponsored for immigration. It takes those visas and uses them for the DACA population and other children brought to the U.S. illegally as minors by their parents.

In terms of enforcement, the bill allows the Department of Homeland Security to detain more people and deport them faster, and it increases the threshold for people attempting to claim asylum, with a goal of reducing fraudulent claims that have clogged the system.

Republican leaders tucked in a fix for the family separation issue, allowing the government to hold children and their parents in immigration detention facilities for longer than 20 days. The bill also says that illegal immigrant parents charged with misdemeanors, who normally would be sent to the criminal justice system’s jails, can be held in immigration detention — meaning they can remain with their children.

House Speaker Paul D. Ryan, Wisconsin Republican, told The Washington Times that Mr. Trump got a good reception from the party.

“It was great,” he said.

Outside the meeting, a group of Democrats marched along the corridors holding signs that said, “Families Belong Together,” and that depicted some of the now-iconic photos of children and their parents at the border.

As the president walked through one of the Capitol’s corridors, a heckler shouted at him, “Mr. President, F– you!” An NBC reporter said on Twitter that the culprit was a congressional intern.

Earlier Tuesday, some of the president’s key supporters warned him against embracing the bill.

The National ICE Council, the union that represents officers at U.S. Immigration and Customs Enforcement, said the bill falls short on a number of the president’s campaign promises.

Chris Crane, the council president, wrote a letter to Mr. Trump saying the bill would open the door to massive fraud, would allow people who defy judges’ deportation orders to get on a pathway to citizenship and would fail to make good on Mr. Trump’s promise of a deportation force of 10,000 more Immigration and Customs Enforcement officers.

He labeled the bill the “Ryan amnesty” and said it repeats the mistakes of the failed 2013 “Gang of 8” immigration bill.

“You pledged publicly to ‘have the backs’ of the men and women of ICE law enforcement. I am asking you to keep that promise,” Mr. Crane wrote.

The ICE Council endorsed Mr. Trump on the campaign trail in 2016.

Rep. Bob Goodlatte, Virginia Republican, said he is “sympathetic to their concerns” but that the compromise is better than alternative proposals that they would have hated.

“But we really have to do something that can get to 218 votes, and some of the people who are in that negotiation did not support their request,” Mr. Goodlatte said. “This happened very quickly, and if they don’t think they were consulted enough, I understand that.”

The White House did not respond to questions about the letter.

Republican leaders plan two votes this week.

One would be on an enforcement-heavy bill written months ago by Mr. Goodlatte and Rep. Michael T. McCaul, Texas Republican. Both chair key committees. That bill includes a renewable DACA permit but doesn’t give Dreamers a pathway to citizenship. It does include a host of new enforcement measures such as requiring employers to use E-Verify to check their hires, cracking down on sanctuary cities and making it a misdemeanor to overstay a visa.

Those measures went too far for many Republicans, and the Goodlatte bill struggled to reach 218 supporters.

So Republican leaders pushed Mr. Goodlatte, Mr. McCaul and moderate lawmakers to work on the compromise bill.

Mr. Trump had backed the enforcement-heavy bill, but his full-throated support for the compromise was critical.

“Folks that would have been against it, I think it’s harder for them to be against it now,” said Rep. Bill Flores, Texas Republican. “I think he probably changed a lot of minds.”

• Stephen Dinan contributed to this article.

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