WASHINGTON — The Capitol Police force is preparing for another assault on the Capitol building on Thursday after obtaining intelligence of a potential plot by a militia group, just two months after a mob of Trump loyalists and extremists attacked the building, leaving five dead and hundreds injured.

Leaving nothing to chance, House leaders on Wednesday abruptly moved a vote on policing legislation from Thursday to Wednesday night, so lawmakers could leave town, according to a senior Democratic aide familiar with the planning.

The “possible” plot, as described by the Capitol Police, appeared to be inspired by the pro-Trump conspiracy theory known as QAnon, according to a senior administration official who reviewed the intelligence warning. Intelligence analysts had spent weeks tracking online chatter by some QAnon adherents who have latched on to March 4 — the original inauguration date set in the Constitution — as the day Donald J. Trump would be restored to the presidency and renew his crusade against America’s enemies.

Some federal officials described the threats as more “aspirational” than operational. The militia group was not named, and even many influential QAnon followers, who believe the United States is dominated by a cabal of Satan-worshiping pedophiles, have cast March 4 as a “deep state” plot to incite the movement’s adherents and provoke a nationwide crackdown.

But after being caught flat-footed by rioters on Jan. 6, the Capitol Police and members of Congress appeared to be taking no chances. Representative Michael McCaul of Texas, a senior Republican on the House Homeland Security Committee, pleaded on CNN on Wednesday: “President Trump has a responsibility to tell them to stand down. This threat is credible. It’s real. It’s a right-wing militia group.”

The perimeter of the Capitol had already been ringed with new fencing, topped with razor wire. The Capitol Police said the agency is now reaching out to local, state and federal law enforcement agencies to prepare further.

“We have obtained intelligence that shows a possible plot to breach the Capitol by an identified militia group on Thursday, March 4,” the force said in a statement. “We are taking the intelligence seriously.”

Skittish lawmakers, many still rattled by the January attack that sent them fleeing, were given plenty of warning this time. Yogananda D. Pittman, the acting chief of the Capitol Police, told lawmakers on Wednesday that the agency had received “concerning” intelligence about possible threats against the Capitol on March 4, adding that threats against lawmakers were “through the roof.” The Capitol Police later sent an alert to lawmakers warning that the force was “monitoring various reports referencing potential First Amendment activities from March 4 to March 6.”

Melissa Smislova, the acting under secretary of the Department of Homeland Security’s intelligence branch, told senators on Wednesday that the department and the F.B.I. had the night before issued an intelligence bulletin about “extremists discussing March 4 and March 6.”

While the warning did not definitively say militia groups planned to come to Washington, the analysts said that continued false statements of election fraud and narratives elevated by QAnon “may contribute” to extremists turning to violence. Those extremists were inspired to target March 4 by QAnon conspiracists who said Mr. Trump would be inaugurated on that date and eventually “return to power,” according to an official who requested anonymity to discuss the warning.

Two federal law enforcement officials said broad concerns about potential violence were warranted, given the online chatter around the QAnon conspiracy and talk of an attack. But they said they had not seen or been briefed on any specific, credible threat of an attack on politicians, the Capitol or other symbols of government.

While they felt it was unlikely that an organized militia group would be able to execute the kind of attack on the Capitol described in the Capitol Police bulletin, particularly given the fortifications around Washington, they did not rule out the possibility that “lone wolf” attackers could try to wreak havoc.

Intelligence officials are struggling to determine whether suspicious online chatter should prompt public warnings about an attack that may not come to fruition. The issue is thorny given that much of that kind of chatter is protected by the First Amendment.

Federal officials decided this time to have a more “forward leaning” approach to information sharing after federal agencies faced widespread backlash for the failed security response on Jan. 6, according to the official.

The warning shared with the Capitol Police emphasized what top federal law enforcement officials have repeatedly said since Jan. 6: that the United States generally faces an elevated threat from domestic extremists emboldened by the attack on Congress.

Ms. Pittman said threats against lawmakers had risen nearly 94 percent in the first two months of the year compared with the first two months of 2020. She assured members of Congress that the police force would be ready for any potential violence on March 4.

Christopher A. Wray, the F.B.I. director, told senators on Tuesday that the Jan. 6 attack was domestic terrorism and that such a threat was “metastasizing across the country.” In a rare terrorism bulletin in January, the Homeland Security Department warned that the attack would not be an isolated episode and that extremists were motivated by “the presidential transition, as well as other perceived grievances fueled by false narratives,” a clear reference to the accusations made by Mr. Trump.

At the Conservative Political Action Conference on Sunday, his first public appearance since leaving office, Mr. Trump repeated his false claim that he had won the November election.

Officials did not specify which militia group they believed was plotting to attack the Capitol on Thursday. The Capitol Police are asking for almost $620 million for the agency’s budget, an increase of nearly 21 percent over current levels, to pay for new equipment, training and an additional 212 officers for assignments such as a permanent backup force to respond to events like the Jan. 6 riot. Ms. Pittman told the lawmakers that she would be working with the architect of the Capitol to design more “physical hardening” of the building after it was overrun by the rioters.

“The U.S.C.P. is steadfast in ensuring that an incident of this nature will never occur again,” she said, adding that “a similar incident occurring in the current environment is a very real and present danger.”

QAnon’s central tenet is that Mr. Trump was elected to take on a cabal of Democrats, international financiers and deep-state bureaucrats who worship Satan, abuse children and seek to dominate the world. When that did not come to pass while Mr. Trump was in office, some QAnon adherents began spinning elaborate conspiracy theories around March 4.

The theory, like much associated with QAnon, is convoluted and takes on various forms, at times including secret pardons issued by President Barack Obama, the Banking Act of 1871, the Emergency Broadcast System and Mr. Trump taking the helm of a newly restored republic. And those are not even the most outlandish elements.

The theory is far from universally accepted among QAnon adherents. A number of the movement’s most influential voices have cast the March 4 theory as a conspiracy within a conspiracy, insisting it was a trap set by the movement’s enemies.

“March 4 is the media’s baby. Nothing will happen,” one QAnon influencer wrote Tuesday on the messaging app Telegram.

Other QAnon followers encouraged their compatriots to be patient. “In time, you’ll feel and see the uprisings around you, You’ll know when it’s safe,” one wrote on Telegram. “March 4 in DC is not safe.”

One meme making the rounds on social media asserted that China’s Communist Party — a favorite QAnon target — and other “bad guys” were spreading the March 4 rumors to incite QAnon followers. “Don’t fall for that. They’ll make sure to turn any peaceful protest into a riot,” it reads.

The meme also plays on the thoroughly debunked notion that anti-Trump forces staged the Jan. 6 attack. “Don’t let them fabricate another ‘Capitol Riot,’” the meme says. “Alert others.”

But in a sign that at least some people believe there is a reason to be in Washington on Thursday, rates at the Trump International Hotel for March 3 and 4 have spiked to three or four times their usual prices, much as they did before Jan. 6.

Reporting was contributed by Adam Goldman, Luke Broadwater, Katie Benner, Carl Hulse, Nicholas Fandos and Ben Decker.