For years, Brendan Hunt had posted wild conspiracy theories on social media platforms and his own website, asserting, among other things, that the rock star Kurt Cobain was murdered and that the Sandy Hook massacre was a hoax.

A decade ago, he took part in the Occupy Wall Street protests against income inequality. More recently, he was a fervent supporter of President Trump, posting several videos in support of Mr. Trump’s false claims that the election had been rigged against him through vote fraud.

On Tuesday, it became clear that Mr. Hunt’s online statements had gotten the authorities’ attention. He was arrested on federal charges of making death threats against prominent Democratic politicians, including Senator Chuck Schumer, Speaker Nancy Pelosi and Representative Alexandria Ocasio-Cortez.

Not only did Mr. Hunt, 37, an assistant analyst for New York’s court system, call last month for the “public execution” of Democratic leaders, he also urged Mr. Trump’s supporters to massacre members of Congress before Inauguration Day, according to a criminal complaint.

He was arrested at his home in Ridgewood, Queens, early Tuesday. He faces up to 10 years in prison if convicted.

Since the Capitol riot on Jan. 6, many people with histories of posting vitriolic threats against public figures with relative impunity have come under greater scrutiny from the federal authorities.

Although Mr. Hunt did not participate in the attack on the Capitol, his arrest underscored the scope of the federal government’s crackdown on social media comments that incite violence. Several people who posted on social media during the Jan. 6 riot are among the dozens who have been charged by federal authorities with taking part in the violent rampage.

Last week, the authorities arrested another Queens man, Eduard Florea, who was not in Washington on Jan. 6 but who posted threatening messages on the social network Parler. Among the messages that caused concern was one in which he suggested that the Rev. Raphael Warnock of Georgia, who was recently elected to the U.S. Senate, should be killed.

Mr. Florea, who had a previous weapons conviction, was charged with illegally possessing ammunition after the authorities found thousands of rounds of rifle ammunition and a stockpile of knives at this home in Middle Village, Queens.

Mr. Hunt’s threats included one posted on Facebook on Dec. 6 in which he said that Mr. Trump’s supporters “want actual revenge on democrats” and urged the president to execute Mr. Schumer, Ms. Pelosi and Ms. Ocasio-Cortez, according to the complaint.

“And if you dont do it, the citizenry will,” Mr. Hunt wrote, the complaint says. “We’re not voting in another rigged election. Start up the firing squads, mow down these commies, and lets take america back!”

In a second post, he said the three Democrats were the sort of “high value targets” that Mr. Trump’s supporters should attack. “They really need to be put down,” he wrote, according to the complaint. “These commies will see death before they see us surrender!”

Mr. Hunt made his first appearance in Federal District Court in Brooklyn on Tuesday at a hearing conducted remotely.

“These threats would be grave under any circumstances, but they’re even more so in the volatile environment we find ourselves in today leading up to the inauguration,” David Kessler, a federal prosecutor, said at the hearing.

Arguing for Mr. Hunt to be released on bail, Mr. Hunt’s lawyer, Leticia Olivera, said he did not have a criminal record, was not a member of a militia or paramilitary group and did not plan on harming federal officials in Washington.

“The allegations in the complaint do not suggest anything other than a plan to make outlandish posts online from inside his home,” Ms. Olivera said.

The federal magistrate judge hearing the matter, Ramon Reyes Jr., ordered that Mr. Hunt be held without bail until trial.

Lucian Chalfen, a spokesman for the state court system, said Mr. Hunt had been suspended without pay from his $57,800-a-year position as an assistant court analyst in the Attorney Registration Unit.

Before retiring, Mr. Hunt’s father was a family court judge in Queens, Mr. Chalfen said. Mr. Hunt is the second person with ties to the state judiciary to be arrested this month. Aaron Mostofsky, whose father is a judge in Brooklyn, was charged this month with taking part in the Capitol riot.

Mr. Hunt has dabbled in acting and filmmaking and has often used the alias X-ray Ultra on social media, the authorities said. A website for “X-ray Ultra Studios” includes photographs of Mr. Hunt and links to his many social media accounts.

Two days after the Washington riot, Mr. Hunt posted an 88-second video titled “KILL YOUR SENATORS” on BitChute, a video-sharing platform, the complaint says. In the video, he spoke directly to the camera.

“We need to go back to the U.S. Capitol when all of the Senators and a lot of the Representatives are back there,” he said, according to the complaint. “And this time we have to show up with our guns. And we need to slaughter these” people, using an expletive for emphasis.

“If anybody has a gun, give me it, I’ll go there myself and shoot them and kill them,” he said, according to the complaint.

The video was not available on X-ray Ultra’s BitChute channel on Tuesday, but several other videos about the Capitol riot and anti-Semitic conspiracy theories were.

Mr. Hunt also posted threats on Parler, which gained popularity among right-wing users and which went dark after Amazon shut off its service because of violent content, the complaint says.

A Parler account with Mr. Hunt’s name and the user name “@xrayultra” included the message “lets go, jan 20, bring your guns #millionmilitiamarch,” the complaint says.

Mr. Hunt’s YouTube channel lists several videos with the title “STOP THE STEAL = ELECTION 2020.” The videos have thumbnail illustrations that depict Mr. Trump as a king, as the Marvel Comics villain Thanos and as the movie character Rambo.