Prosecutors argue that Trump ‘became the inciter in chief’ and retell riot with explicit video.

House Democrats prosecuting former President Donald J. Trump on Wednesday showed disturbing, never-before-seen video footage of his supporters rampaging into the Capitol last month and searching for former Vice President Mike Pence and Speaker Nancy Pelosi to harm or even kill them.

In powerful images played for a silent, sober Senate chamber, the House managers put the horror of the Jan. 6 siege on vivid display as rioters smashed their way into the building, overwhelmed police officers and marched through the halls seeking to stop the counting of the Electoral College votes and hunt down those perceived as Mr. Trump’s antagonists.

The footage from Capitol security cameras showed Mr. Pence, who alienated Mr. Trump’s supporters by refusing to try to overturn the election, being rushed by Secret Service officers down a staircase to escape invaders calling for his death. Ms. Pelosi’s staff members were shown barricading themselves into an office just minutes before the mob arrived and tried to break down the door.

“They were within 100 feet of where the vice president was sheltering with his family, and they were just feet away from the doors of this chamber where many of you remained at that time,” Stacey Plaskett, a Democratic delegate from the Virgin Islands and one of the House impeachment managers, told the senators sitting as jurors.

She and other managers played police dispatch audio recordings and cited legal filings, social media postings and videos to make clear that the rioters posed a serious danger to Mr. Pence, Ms. Pelosi and other lawmakers as well as to police officers.

“Hang Mike Pence! Hang Mike Pence!” the crowd could be heard chanting. Outside the Capitol, where a gallows had been set up, others called out, “Bring out Pence!” One rioter taped a video saying, “He’s a total treasonous pig.”

They likewise were hunting down Ms. Pelosi, and the man famously photographed sitting at her desk was shown carrying a 950,000-volt stun gun. “Where are you, Nancy?” some called out. “We’re looking for you!”

“Again, that was a mob sent by the president of the United States to stop the certification of an election,” Ms. Plaskett told the Senate.

“President Trump,” she added, “put a target on their backs and his mob broke into the Capitol to hunt them down.”

The new footage came as the House managers formally opened their case that Mr. Trump incited an insurrection by arguing that his provocation began months before the day of the riot, as he propagated a “Big Lie” to persuade supporters that his re-election was being stolen.

“Donald Trump surrendered his role as commander in chief and became the inciter in chief of a dangerous insurrection,” Representative Jamie Raskin, Democrat of Maryland and the lead manager, told the senators.

“He told them to fight like hell,” Mr. Raskin added, “and they brought us hell that day.”

Representative Joe Neguse, Democrat of Colorado and another manager, played clips of Mr. Trump asserting even before the election that “the only way we can lose” is if the other side cheated, priming his base to reject any result other than a victory for him and then egging them on with repeated phrases like “stop the steal” and “fight like hell.”

The managers showed the former president’s messages encouraging backers to come to Washington on Jan. 6 to protest the election results. They also methodically assembled online chats reportedly monitored by Mr. Trump’s operatives in which his supporters used aggressive language suggesting an intent to use violence to stop the Electoral College count.

With his Twitter account suspended, Mr. Trump remained silent on Wednesday and left his case to his lawyers, who did not impress senators in either party with their opening foray on Tuesday and under the bipartisan rules did not speak on Wednesday.

The lawyers have maintained that the former president’s language was protected free speech and hardly incitement of violence or insurrection.

“There is no set of facts that ever justifies abrogating the freedoms granted to Americans in the United States Constitution,” Bruce L. Castor Jr., one of the lawyers, said on Fox News on Wednesday.