It was opening day of the 2021 legislative session, and the perimeter of the Georgia State Capitol on Monday was bristling with state police officers in full camouflage gear, most of them carrying tactical rifles.

On the other side of the country, in Olympia, Wash., dozens of National Guard troops in riot gear and shields formed a phalanx behind a temporary fence. Facing them in the pouring rain was a small group of demonstrators, some also wearing military fatigues and carrying weapons. “Honor your oath!” they shouted. “Fight for freedom every day!”

And in Idaho, Ammon Bundy, an antigovernment activist who once led his supporters in the occupation of a federal wildlife refuge in Oregon, showed up outside the statehouse in Boise with members of his organization carrying “wanted” posters for Gov. Brad Little and others on charges of “treason” and “sedition.”

“At a time of uncertainty, we need our neighbors to stand next to and continue the war that is raging within this country,” Mr. Bundy’s group declared in a message to followers.

State capitals across the country are bracing for a spillover from last week’s violent assault on the U.S. Capitol, with state legislatures already becoming targets for protesters in the tense days around the inauguration of the incoming president, Joseph R. Biden Jr.

Gone is a large measure of the bonhomie that usually accompanies the annual start of the legislative season, replaced by marked unease over the possibility of armed attacks and gaps in security around statehouses that have long prided themselves on being open to constituents.

“Between Covid and the idea that there are people who are armed and making threats and are serious, it was definitely not your normal beginning of session,” said Senator Jennifer A. Jordan, a Democratic legislator in Georgia who watched the police officers assembled outside the State Capitol in Atlanta on Monday from her office window. “Usually folks are happy, talking to each other, and it did not have that feel.”

Dozens of state capitals will be on alert in the coming days, following calls among a mix of antigovernment organizations for actions in all 50 states on Jan. 17. Some of them come from far-right organizations that harbor a broad antigovernment agenda and have already been protesting state Covid-19 lockdowns since last spring. The F.B.I. this week sent a warning to local law enforcement agencies about the potential for armed protests in all 50 state capitals.

In a video news conference on Monday, Gov. Gavin Newsom of California said that “everybody is on high alert” for protests in Sacramento in the days ahead.

The National Guard would be deployed as needed, he said, and the California Highway Patrol, responsible for protecting the Capitol, was also on the lookout for any budding violence. “I can assure you we have a heightened, heightened level of security,” he said.

In Michigan, the state police said they had beefed up their presence around the State Capitol in Lansing and would continue that way for weeks. The commission that oversees the Statehouse voted on Monday to ban the open carry of firearms inside the building, a move Democratic lawmakers had been demanding since last year, when armed protesters challenging government Covid-19 lockdowns stormed the building.

Two of those involved in the protests were later arrested in what the authorities said was a plot to kidnap Gov. Gretchen Whitmer and put her on trial.

Michigan’s attorney general, Dana Nessel, took to Twitter to warn the public away from the Statehouse, saying it was not safe.

Images from the Wisconsin state legislature in Madison showed large sheets of plywood being readied to cover the ground-floor windows. In St. Paul, Minn., the Statehouse has been surrounded by a chicken-wire fence since early last summer, when social justice protests erupted over the killing of George Floyd in neighboring Minneapolis.

Patricia Torres Ray, a Democratic state senator, said the barrier had served to protect the building and the legislators, but concerns remained about possible gaps, such as the system of underground tunnels that link many public buildings in Minnesota to allow people to avoid walking outdoors in the winter.

Gov. Jay Inslee in Washington ordered extra security after an armed crowd of Trump supporters breached the fence at the governor’s mansion last week while he was at home. State troopers intervened to disperse the crowd.

In Texas, Representative Briscoe Cain, a conservative Republican from the Houston suburb of Deer Park, said that the legislature in Austin was likely protected by the fact that so many lawmakers carry firearms.

“I have a pistol on my hip as we speak,” Mr. Cain said in a telephone interview on Monday. “I hope they’re never necessary, but I think it’s why they will never be necessary.”

The Texas Legislature, dominated by Republicans, meets every two years and was scheduled to begin its 140-day session at noon on Tuesday.

There may be efforts to reduce the presence of guns in the Capitol, Mr. Cain said, but he predicted that they would be doomed to failure given widespread support for the Second Amendment.

In Missouri, Dave Schatz, the Republican president of the State Senate, said hundreds of lawmakers had gathered on Monday on the Statehouse lawn in Jefferson City for the swearing-in of Gov. Mike Parson and other top officials. Although security was tight, with the roads around the building closed, the presence of police and other security officers was normal for the day, Mr. Schatz said, and no fellow legislators had buttonholed him so far about increased security.

“We are far removed from the events that occurred in D.C.,” he said.

In Nevada, a Republican leader in Nye County posted a letter on Friday that likened recent protests of the election results across the country to the American Revolution, declaring: “The next 12 days will be something to tell the grandchildren! It’s 1776 all over again!”

The letter — written by Chris Zimmerman, the chairman of the Nye County Republican Central Committee — prompted a rebuke over the weekend from Representative Steven Horsford, a Democrat who represents the county.

Next door in Clark County, Nev., which includes Las Vegas, Democratic officials sent out a public safety alert on Sunday about potential violence across the state, warning, “Over the past 48 hours, the online activity on social media has escalated to the point that we must take these threats seriously.”

While most of the protests announced so far are expected to focus on state capitals, law enforcement and other officials in various cities have said they believe that other government buildings could also be targeted.

Federal authorities said on Monday that they had arrested and charged one man, Cody Melby, with shooting several bullets into the federal courthouse in Portland, Ore., on Friday night. Mr. Melby had also been arrested a couple of days earlier when, the police said, he tried to enter the State Capitol in Salem with a firearm.

Some of those protesting in Oregon and Washington said they were opposed to state lockdown rules that prevent the public from being present when government decisions are being made.

James Harris, 22, who lives in eastern Washington State, said he went to the Capitol in Olympia on Monday to push for residents to be full participants in their state’s response to Covid-19. He said he was against being forced to wear masks and to social distance; the lockdowns are “hurting people,” he said.

Mr. Harris is a truck driver, but he said the virus control measures had prevented him from being able to work since March.

Georgia already has seen trouble in recent days. At the same time that protesters were swarming into the U.S. Capitol in Washington last week, armed Trump supporters appeared outside the statehouse in Georgia. Law enforcement officers escorted to safety the secretary of state, Brad Raffensperger, who had refused President Trump’s attempts to depict the presidential election as fraudulent.

Senator Jordan noted that many of the security measures being put in place, including the construction of a tall iron fence around the Capitol building, were actually decided on during last summer’s social justice demonstrations, when protesters surrounded many government buildings.

Now, she said, the threat is coming from the other end of the political spectrum.

“These people are clearly serious, they are armed, they are dangerous,” Ms. Jordan said, “and from what we saw last week, they really don’t care who they are trying to take out.”

Contributing reporting were David Montgomery, Kathleen Gray, Jill Cowan, Maggie Astor, Adam Goldman and Hallie Golden. Kitty Bennett contributed research.