Mr. Trump’s effusive praise of his chief of staff came during a visit to Pennsylvania where he was appearing to promote his tax cut and boost Rick Saccone, a Republican state legislator running for Congress in a special election in March.

Asked whether he minded Mr. Kelly telling lawmakers he had not been fully informed about immigration, Mr. Trump said: “No, he did not say that. He didn’t say it the way you would like him to say it.”

But according to one person familiar with the president’s thinking, Mr. Trump was livid when he learned that Mr. Kelly had described him as “evolving” in his immigration position. Throughout the evening on Wednesday, Mr. Trump fielded calls from allies who described Mr. Kelly’s comments to Congress as undermining the president, stoking Mr. Trump’s fury.

The president — who never likes it when someone characterizes his thinking — vented his anger to Mr. Kelly and to allies, according to the person familiar with the president’s thinking. It was similar to a moment during the campaign in April of 2016, when Paul Manafort — who had just been hired to the Trump campaign — was caught on tape at a meeting with Republican National Committee members saying of Mr. Trump, “the part he’s been playing is evolving.”

When a president’s chief of staff speaks to members of Congress, it should be a “consistent message,” Representative Henry Cuellar, a Democrat of Texas, said on Thursday in an interview with CNN. Mr. Cuellar, who attended Wednesday’s meeting with Mr. Kelly, said the inconsistency “makes it hard” to negotiate.

Lawmakers who attended the meeting on Wednesday described Mr. Kelly’s remarks. Representative Luis V. Gutiérrez, a Democrat of Illinois who was at the meeting, said Mr. Kelly told the group that “a 50-foot wall from sea to shining sea isn’t what we’re going to build.”

Mr. Gutiérrez told reporters that Mr. Kelly referenced Mr. Trump’s campaign promises to build a wall and said, “There were statements made about the wall that were not informed statements.”

In an interview with Fox News on Wednesday night, Mr. Kelly defended his comments to the Democratic lawmakers and said, “There’s been an evolutionary process that this president has gone through, as a campaign, and I pointed out to all of the members that were in the room that they all say things during the course of campaigns that may or may not be fully informed.”

Mr. Kelly also said the president has “evolved in the way he’s looked at things,” in reference to what should constitute a wall along the southern border.

Congress is currently working on a deal that would protect some 780,000 young immigrants from deportation. During the meeting on Wednesday, Mr. Kelly relayed confidence that negotiations would move forward for a permanent solution to preserve protections under the Deferred Action for Childhood Arrivals program, or DACA, the Obama-era policy that Mr. Trump moved in September to end.

In a Twitter post later on Thursday morning, Mr. Trump said there would be no such deal without a wall.

Donald J. Trump

@realDonaldTrump

We need the Wall for the safety and security of our country. We need the Wall to help stop the massive inflow of drugs from Mexico, now rated the number one most dangerous country in the world. If there is no Wall, there is no Deal!

5:16 AM – Jan 18, 2018

The president had recently started to water down his statements about building a wall and told lawmakers last week that 2,000 miles of wall would not be needed because of natural barriers. The wall is estimated to cost $18 billion over the next 10 years and cover 900 miles of the southern border, according to a spending plan submitted to Congress earlier this year.

The White House director of legislative affairs, Marc T. Short, pushed back against the Democrats’ accounts of Mr. Kelly’s remarks on Wednesday. “I don’t recall General Kelly saying the president was uninformed,” Mr. Short told CNN in an interview.

Accounts of what was said and by whom during recent high-level meetings on immigration policies have already hurt prospects for a broad spending and immigration deal to be achieved by Friday. Some participants in an Oval Office meeting last week said Mr. Trump called African nations “shitholes” in a discussion about immigration, reigniting concerns about the president’s racially tinged language about immigrants. Others said the president used the term “shithouse.”

The absence of an agreement could lead to a government shutdown, a risk that Mr. Trump may have increased later on Thursday morning when he wrote another Twitter post that blew up Republican plans to keep the government running.

Democrats have said they will not support a government spending plan that does not address the fate of the young immigrants, known as Dreamers, who could face deportation as soon as March.

Mr. Trump’s morning Twitter posts and his anger with Mr. Kelly about his chief of staff’s remarks to lawmakers come after weeks of the president fielding complaints from allies and staff members about Mr. Kelly’s restrictive influence. Mr. Trump has heard repeatedly that Mr. Kelly is trying to isolate him, and that senior aides to the president are frustrated that they cannot speak directly to Mr. Trump and must go through a filter.

People have warned the president that he faces a massive staff exodus among senior officials, in part as a result of the working environment that Mr. Kelly has created.