A Georgia man who had an assault rifle and was headed to Washington for the Jan. 6 pro-Trump rally at the U.S. Capitol pleaded guilty on Friday to sending threatening text messages about House Speaker Nancy Pelosi.

The man, Cleveland Grover Meredith Jr., wrote to an acquaintance the day after the violent attack on the U.S. Capitol that he would put “a bullet in her noggin on Live TV” and included a purple devil emoji, the federal authorities said. In other messages, he said he would run over Ms. Pelosi.

“I predict that within 12 days, many in our country will die,” he wrote.

Mr. Meredith had been staying at a Holiday Inn in Washington and had weapons in his camper-style trailer, including a Glock handgun, a Tavor X95 assault rifle and thousands of rounds of ammunition, according to court records.

Mr. Meredith was one of the first 13 people charged in federal court after a mob in support of former President Donald J. Trump stormed the Capitol. He was charged in January with transmitting a threat in interstate commerce, possession of an unregistered firearm and unlawful possession of ammunition, according to court records.

Mr. Meredith pleaded guilty to the interstate communications charge and faces a maximum of five years in prison and a $250,000 fine.

Under a plea agreement, he is expected to face up to two years in prison and a fine of up to $75,000, according to court documents. His sentencing is scheduled for December. Messages left for his lawyer, Paul Kiyonaga, were not immediately returned on Saturday.

The Atlanta Journal-Constitution reported that Mr. Meredith had erected a billboard in 2018 in Acworth, Ga., that read, “#QANON” along with the name of his business, Car Nutz Car Wash.

The QAnon conspiracy theory, which the F.B.I. has labeled a potential domestic terrorism threat, accuses Democrats and some Republicans of being beholden to a cabal of entrenched political insiders, pedophiles and Satanists. Many followers believe that Mr. Trump was secretly battling a criminal band of sex traffickers.

Mr. Meredith had missed the Capitol riot itself because he arrived in Washington too late while driving from Colorado, he told investigators.

The Journal-Constitution reported that U.S. District Court Judge Amy Berman Jackson on Friday asked Mr. Meredith if he wrote a text threatening to kill Ms. Pelosi.

“It was political hyperbole,” Mr. Meredith told the judge. “But I did text that.”

The federal authorities have said they are committed to holding to account anyone responsible for the “disgraceful criminal acts” related to the assault on the Capitol.

“To be clear, what took place that day was not First Amendment-protected activity, but rather an affront to our democracy,” the F.B.I. director, Christopher Wray, said in January, after Mr. Meredith and others had been charged. “We will continue to aggressively investigate each and every individual who chose to ignore the law and instead incite violence, destroy property and injure others.”