President Trump and new chief of staff John F. Kelly ousted Chief White House Strategist Steve Bannon Friday, jettisoning the adviser who was viewed as the president’s key link to the “alt-right” movement and white nationalism.

The White House portrayed the move as a mutual parting.

“White House Chief of Staff John Kelly and Steve Bannon have mutually agreed today would be Steve’s last day,” said White House press secretary Sarah Huckabee Sanders. “We are grateful for his service and wish him the best.”

The ouster of Mr. Bannon comes less than a month after the president hired Mr. Kelly as his chief of staff to impose order in a chaotic West Wing distracted by internal feuds. Mr. Kelly, who replaced Chief of Staff Reince Priebus, fired Communications Director Anthony Scaramucci as one of his first moves.

White House staffers and others close to the West Wing said Mr. Kelly, a retired general who formerly led the Department of Homeland Security, was clearly the force who pushed out Mr. Bannon.

“Staffers are relieved to see that the effort by Gen. Kelly is ongoing to professionalize operations within the White House,” said a Republican close to the West Wing.

Just Tuesday, Mr. Trump had said “we’ll see what happens” when asked about Mr. Bannon’s future.

The calls for Mr. Bannon’s firing intensified in the past week, after a white nationalist rally in Charlottesville, Virginia, turned violent, leaving one woman dead and 19 injured. The president has blamed “both sides” for the violence, and the resulting furor has targeted Mr. Bannon as the adviser most responsible for Mr. Trump appearing to cozy up with the alt-right movement.

House Minority Leader Nancy Pelosi of California said Mr. Bannon’s departure is “welcome news,” but she said it “doesn’t disguise where President Trump himself stands on white supremacists.”

“Personnel changes are worthless so long as President Trump continues to advance policies that disgrace our cherished American values,” Mrs. Pelosi said in a statement.

One point of continual friction has been Mr. Bannon’s rivalry with a more moderate wing of advisers that Bannon allies refer to as “West Wing Democrats” — including chief economic adviser Gary Cohn, presidential son-in-law Jared Kushner and Mr. Trump’s daughter, Ivanka.

Mr. Bannon is credited by many with serving as the architect of Mr. Trump’s winning campaign of “economic nationalism,” although the president has bristled at the suggestion and has stated repeatedly that he himself deserves credit for his win. On Tuesday, the president reminded reporters that Mr. Bannon came to his campaign “very late” after Mr. Trump had already won the GOP primaries.

Just as the news broke Friday, a group of influential conservatives had sent a letter to Mr. Trump affirming Mr. Bannon’s value in “keeping your agenda front and center.”

Americans for Limited Government President Rick Manning, who signed the letter, said later Friday that conservatives are very disappointed by the ouster of Mr. Bannon.

“Steve Bannon is and has been a critical part of the Trump administration’s many successes,” Mr. Manning said. “There’s obviously some concern that there won’t be an effective counterweight to the Gary Cohns. Our encouragement to [Mr. Trump] would be to make certain that there is somebody close to him who shares his philosophy and understands his key issues and how they translated to the American people.”

Mr. Bannon generated headlines twice this week, being blamed for encouraging white nationalists’ support of Mr. Trump while he served as head of Breitbart News, a role that has drawn negative news coverage as the president tried address the causes of the violence in Virginia.

Next, Mr. Bannon was quoted in an article in The American Prospect, undermining Mr. Trump’s threats of potential military action against North Korea by saying it was essentially a bluff.

He also welcomed Democrats’ playing “identity politics” with race, saying Mr. Trump would end up a political winner in that equation.

“Ethno-nationalism — it’s losers,” Mr. Bannon said. “It’s a fringe element. I think the media plays it up too much, and we gotta help crush it, you know, uh, help crush it more. These guys are a collection of clowns.”

Another internal war in the White House was between Mr. Bannon and national security adviser H.R. McMaster, an Army general who has been accused by some conservatives as an Obama sympathizer and a “globalist.”

Mr. Bannon was viewed with suspicion by his rivals in the West Wing as having encouraged a campaign on social media and on Breitbart to get Mr. McMaster fired.

Democrats and progressive groups rejoiced at Mr. Bannon’s ouster.

“There is one less white supremacist in the White House, but that doesn’t change the man sitting behind the Resolute desk,” said Democratic National Committee spokesman Michael Tyler. “Donald Trump has spent decades fueling hate in communities, including his recent attempts to divide our country and give a voice to white supremacists. We need leaders who represent all of us and the diversity of our country.”

Sierra Club Executive Director Michael Brune said “Good riddance to Steve Bannon.”

“His disgraceful brand of hate and vitriol deserves no place in the White House,” Mr. Brune said. “Yet, no one should forget that it was Donald Trump who enabled Bannon.”

Rep. David Cicilline, Rhode Island Democrat, said Mr. Bannon’s departure “cannot wash away the harm he and the president have done.”

“It can’t reverse the Muslim ban,” Mr. Cicilline said. “It can’t reverse the president’s inappropriate attacks on a federal judge of Mexican heritage. And it can’t reverse the White House’s reluctance to denounce white supremacists.”

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