WASHINGTON — President Trump on Wednesday offered encouragement to proponents of QAnon, a viral conspiracy theory that has gained a widespread following among people who believe the president is secretly battling a criminal band of sex traffickers, and suggested that its proponents were patriots upset with unrest in Democratic cities.

“I’ve heard these are people that love our country,” Mr. Trump said during a White House news conference ostensibly about the coronavirus. “So I don’t know really anything about it other than they do supposedly like me.”

When told by a reporter about the central premise of the QAnon theory — a belief that Mr. Trump is saving the world from a satanic cult made up of pedophiles and cannibals connected to Democratic Party figures, so-called deep-state actors and Hollywood celebrities — Mr. Trump did not question the validity of the movement or the truth of those claims.

Instead, he offered his help.

“Is that supposed to be a bad thing or a good thing?” the president said lightly, responding to a reporter who asked if he could support that theory. “If I can help save the world from problems, I am willing to do it. I’m willing to put myself out there.”

Mr. Trump’s cavalier response was a remarkable public expression of support for conspiracy theorists who have operated in the darkest corners of the internet and have at times been charged with domestic terrorism and planned kidnapping.

“QAnon conspiracy theorists spread disinformation and foster a climate of extremism and paranoia, which in some cases has led to violence. Condemning this movement should not be difficult,” said Jonathan A. Greenblatt, the chief executive of the Anti-Defamation League. “It’s downright dangerous when a leader not only refuses to do so, but also wonders whether what they are doing is ‘a good thing.’”

Mr. Trump’s comments also elevated a group of people who the F.B.I. has said poses a domestic terrorism threat.

“QAnon is promoting political disinformation, medical disinformation and carrying on a legacy of anti-Semitic tropes,” Joan Donovan, the research director at the Shorenstein Center on Media, Politics and Public Policy, said in an interview. “Attention from the president is only going to embolden these groups to grow their ranks.”

Although a majority of Americans say they remain unfamiliar with the particulars of the movement — research shows that people who use social media platforms like Twitter and Reddit are more likely to be familiar with QAnon — those who study the behavior of fringe groups have warned of the power to produce extremism among followers.

QAnon is a larger and many-tentacled version of the Pizzagate conspiracy theory, which falsely claimed that Hillary Clinton was operating a child sex-trafficking ring out of the basement of a Washington, D.C., pizza restaurant. In December 2016, a man who said he was on the hunt for proof of child abuse was arrested after firing a rifle inside the restaurant.

QAnon supporters often flood social media pages with memes and YouTube videos that target well-known figures — like Mrs. Clinton and her husband, former President Bill Clinton, and the actor Tom Hanks — with unfounded claims about their links to child abuse. Lately, activists have used anti-child-trafficking hashtags as a recruitment tool.

“It’s not just a conspiracy theory, this is a domestic extremist movement,” said Travis View, a host of “QAnon Anonymous,” a podcast that seeks to explain the movement. Mr. View said that Twitter and Facebook pages exploded with comments from gleeful followers after Mr. Trump’s comments.

Mr. View pointed out that the president answered the question by supporting the central premise of the QAnon theory — that he is battling a cabal of left-wing pedophiles — rather than addressing the lack of evidence behind the movement.

“They are very practiced at trying to interpret any comment from Trump as validation,” Mr. View said of the movement’s followers. “And Trump very coyly indicated he would help if he could.”

In recent weeks, platforms including Twitter and Facebook have rushed to dismantle a mushrooming number of QAnon-related accounts and fan pages, a move that people who study the movement say is too little and too late. On Wednesday, after a record amount of QAnon-related growth on the site, Facebook said it removed 790 QAnon groups and was restricting another 1,950 groups, 440 pages and more than 10,000 Instagram accounts.

On Facebook alone, activity on some of the largest QAnon groups rose 200 to 300 percent in the past six months, according to data gathered by The New York Times.

“We have seen growing movements that, while not directly organizing violence, have celebrated violent acts, shown that they have weapons and suggest they will use them, or have individual followers with patterns of violent behavior,” Facebook said in a statement, adding that it would also block QAnon hashtags like #digitalarmy and #thestorm.

But the movement made the jump from social media long ago: With dozens of QAnon supporters running this year for Congress — including several who have won Republican primaries in Oregon and Georgia — QAnon is knocking on the door of mainstream politics, and has done so with the president’s help.

QAnon’s origins are murky. In October 2017, a post appeared on the 4chan message board from an anonymous account calling itself “Q Clearance Patriot.” This poster, who became known simply as “Q,” claimed to be an intelligence officer with access to classified information about a war Mr. Trump was waging against the global cabal.

According to QAnon lore, Mr. Trump was recruited by top military generals to run for president in 2016 in order to break up the cabal’s criminal conspiracy, end its control of politics and the media, and bring its members to justice.

It has also incorporated elements of other conspiracy theories, including claims about the assassination of President John F. Kennedy, the existence of U.F.O.s and the 9/11 “truther” movement.

For years, Mr. Trump and his campaign have flirted with the QAnon movement. Kayleigh McEnany, the White House press secretary, has interviewed supporters in her role as a spokeswoman for the Trump campaign, creating footage that was later promoted to Mr. Trump’s supporters.

“If you could say one thing to the president, what would you say?” Ms. McEnany said to a supporter outside a campaign rally in February as several attendees shouted, “Q!” The two talked about what it meant to be a “digital soldier” for Mr. Trump.

“Who is Q?” the man replied. Ms. McEnany said that she would pass the message along.

For his part, the president has often reposted QAnon-centric content into his Twitter feed. And QAnon followers have long interpreted messages from Dan Scavino, the White House director of social media, as promoting tongue-in-cheek symbols associated with the movement.

“I’m not surprised at all by his reaction, and I don’t think QAnon conspirators are surprised either. It’s terrifying,” Vanessa Bouché, an associate professor of political science at Texas Christian University, said in an interview. “In a democratic society, we make decisions based on information. And if people are believing these lies, then we’re in a very dangerous position.”

Last week, Mr. Trump tweeted his support of Marjorie Taylor Greene, a QAnon follower who won her House primary runoff in Georgia, but he declined to directly embrace the movement itself during a White House news conference.

“She won by a lot,” he said. “She comes from a great state.”

But on Twitter, Mr. Trump endorsed Ms. Greene, calling her a “future Republican Star” and “a real WINNER!”

Katie Rogers reported from Washington, and Kevin Roose from San Francisco. Sheera Frenkel contributed reporting from San Francisco.