Federal and local authorities across the country pressed their hunt over the weekend for the members of the angry mob that stormed the Capitol building last Wednesday, as Washington’s mayor issued an urgent appeal to start preparing immediately for more potential violence before, during and after the inauguration of President-elect Joe Biden.

Following one of the most stunning security lapses in the city’s history, Mayor Muriel E. Bowser sent a firmly worded letter Saturday to the Department of Homeland Security, asking officials to move up to Monday the implementation of heightened security measures that are otherwise set to begin Jan. 19, just one day before Biden’s swearing-in.

Bowser’s call to action, which came as law enforcement officers in several states made arrests related to the assault on the Capitol, was echoed today by Sen. Roy Blunt, R-Mo., who is charged with overseeing the planning of the inaugural celebration.

The Capitol complex, typically a hive of activity, remained cut off from its surroundings tonight by troop deployments and an imposing scrim of 7-foot-tall, unscalable fencing.

Still in shock from the worst breach of the building in more than two centuries, lawmakers were expected to turn their attention this week to a second slate of impeachment charges against President Donald Trump, who has said little about the riots he helped incite — in part because social media companies, like Twitter and Facebook, have either banned him or severely limited his use of their platforms.

Security experts warned over the weekend that some far-right extremist groups have now started to focus attention on Inauguration Day and are already discussing an assault similar to the one on the Capitol, which led to the sacking of congressional offices and the deaths of at least five people, including a Capitol Police officer.

As of Sunday, nearly 400 people had joined a private group online dedicated to what is being billed as the “Million Militia March,” an event scheduled to take place in Washington on Jan. 20. On Parler, a social media site popular on the far right that is in danger of being taken offline because of rampant talk of violence, commenters were debating what tools they should bring to the march, mentioning everything from baseball bats to body armor to assault rifles.

“We took the building once,” one person posted. “We can take it again.”

While most of the chatter online appears to be directed toward Inauguration Day, some on the right have argued that pro-Trump activists should instead gather once again on Capitol Hill and hold other rallies in cities outside Washington on Jan. 17. Over the weekend, flyers began to circulate on Parler and in private groups on the chatting services WhatsApp and Signal, calling for an “Armed march on Capitol Hill and all state capitols” at noon that day.

“I’d like to come to this, but want to know, does our president want us there?” asked one person on the social media site Gab. “Awaiting instructions.”

In a statement, the U.S. Secret Service, which is responsible for security at the inauguration, said the inauguration was “a foundational element of our democracy” and “the safety and security of all those participating” was “of the utmost importance.”

In a separate statement, Rep. Jason Crow, D-Colo., a former Army Ranger, said he had spoken with military officials who were aware of “possible threats posed by would-be terrorists” in the coming days and were working with local and federal law enforcements officers to prevent them.

Even as the throng of hundreds — if not thousands — breached gates, smashed windows and stormed into the Capitol last week, there were also tense standoffs at statehouses in Kansas, Colorado, Oregon and Georgia.

On Saturday, that trend seemed to continue as Sen. Charles E. Grassley, R-Iowa, said he was told of a “disturbing report of a death threat” received Friday by the Iowa Democratic Party.

“Threats like this & violence are UNACCEPTABLE,” Grassley wrote on Twitter.

On Monday, the Michigan Capitol Commission is scheduled to meet to consider banning guns from the building. In April, in a kind of dress rehearsal for the chaos in Washington, a group of gun-toting protesters decrying coronavirus lockdowns rushed the state Capitol in Lansing, not long after Trump tweeted, “Liberate Michigan.”

Armed with federal warrants, law enforcement officers spent much of the weekend cracking down on members of the mob in Washington, making a series of arrests in states from Iowa to Florida, and filing new charges against some of the more than 80 people who were taken into custody last week by local officers in Washington. Among those charged have been a man seen hauling off House Speaker Nancy Pelosi’s lectern; Nicholas Ochs, the leader of the Hawaii chapter of the far-right nationalist group the Proud Boys; and a proponent of the QAnon conspiracy theory known for showing up at pro-Trump rallies in a headdress with horns and a spear.

On Saturday, federal prosecutors filed a new complaint against Cleveland Grover Meredith Jr., a Georgia man who was accused of threatening Pelosi by saying in a text message that he was going to put “a bullet in her noggin on Live TV.” Federal agents said that Meredith had been staying at a Holiday Inn in Washington and had weapons in his camper-style trailer that included a Glock handgun, a Tavor X95 assault rifle and hundreds of rounds of ammunition.

Today, prosecutors brought charges of violent entry and disorderly conduct against a figure who had first been identified online by civilian sleuths: Eric G. Munchel of Nashville, Tennessee. In a photograph that circulated widely after the attack, Munchel, 30, was pictured wearing tactical military gear and carrying a handful of plastic restraints known as zip ties.

Prosecutors in Washington also filed a complaint today on similar charges against Larry R. Brock, a retired Air Force officer from Texas, saying he too had been carrying plastic restraints.

The FBI has said that it has received more than 40,000 tips online about the riots, including photographs and video clips. In an interview with NPR on Sunday, Michael R. Sherwin, the U.S. attorney in Washington, said that the Justice Department was considering charges for “theft of national security information” after some in the mob looted laptops, documents and other items from congressional offices.

Some of those who had been at the Capitol discovered that they had been put on government no-fly lists as they tried Sunday to make their way home from Washington.

As charges continued to be filed, more participants in the attack were identified around the country, among them business executives and local school board officials. Several police departments — and the New York Fire Department — have said they are investigating members who may have taken part in the assault.

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