"While the majority of Republicans in the Senate abdicated their responsibility to hold the President accountable, we must hold him accountable for the insurrection that he so blatantly planned," Thompson said. "Failure to do so will only invite this type of authoritarianism for the anti-democratic forces on the far right that are so intent on destroying our country."

Jason Miller, a spokesman for Trump, said the former President did not incite or work to incite riots at the Capitol.

"President Trump has been acquitted in the Democrats' latest Impeachment Witch Hunt, and the facts are irrefutable," Miller said in a statement. "President Trump did not plan, produce or organize the Jan. 6th rally on the Ellipse. President Trump did not incite or conspire to incite any violence at the Capitol on Jan. 6th."

Giuliani did not immediately respond to a request for comment.

The Civil War era statute mentioned in the lawsuit is scarcely used but reflects historic efforts to thwart members of Congress.

Here is what we know about it.

WHAT DOES THE 1871 KU KLUX KLAN ACT DO?

The federal statute was passed after the Civil War to combat violence by the KKK and allow civil action to be taken against people who use "force, intimidation, or threat" to prevent anyone from upholding the duties of their office. It bans people from engaging in conspiracies and violence to block members of Congress from doing their jobs.

Jon Greenbaum, chief counsel and senior deputy director for the Lawyers' Committee for Civil Rights, said that the Ku Klux Klan Act is used when there are specific threats, including actions that threaten the right to vote and prevent federal officers from doing their jobs.

"If you have the right facts it's something that can be a powerful tool," Greenbaum said. "I don't think people necessarily understand the Ku Klux Klan Act very well because it isn't something that has been used that much, it's a pretty technical statute and of course, it applies more broadly than to Ku Klux Klan activities."

Joseph Sellers, an attorney representing Thompson and the NAACP in the lawsuit, called Trump, Giuliani and the two groups the "principal architects" of the insurrection and said the historic KKK law should be used to protect Congress members who were impacted that day.

"Unfortunately, we are again needing to invoke the same statute to ensure protections with members of Congress who were threatened and subjected to intimidation," Sellers said Tuesday. "As you heard Congressman Thompson speak about, suffered real harm during the course of the insurrection and other events that gave rise to it."

WHAT IS THE HISTORY BEHIND THE LAW?

At the time it was passed, the law was intended to protect Black people and members of Congress from being terrorized by the KKK. The KKK had particularly been known to use threats, assaults and destruction to influence elections and intimidate White Republicans who were attempting to participate in the reunited National Congress. The group also sought to reverse and block Reconstruction-era activities in the South that gave Black people political power and civil rights.

"It was specifically meant to provide federal civil remedies for federal officers who were prevented from performing their duties by two or more individuals, whether federal marshals in the post-Civil War South, federal judges in un-reconstructed lower courts; or federal legislators," University of Texas Law professor and Supreme Court analyst Stephen Vladeck said.

Vladeck, who's also a CNN contributor, said the provisions of the law can easily be applied to the Jan. 6 riots given that two or more people conspired to stop Congress from "performing its constitutional function of certifying President Biden's Electoral College victory."

Aziz Huq, a professor of law at the University of Chicago and a former civil rights attorney, said the Ku Klux Klan Act was a response to the emergence of the KKK as a kind of instrument for reestablishing racial hierarchies in the South.

Huq said that initially the law lost momentum because the Supreme Court had a series of rulings that were very hostile, particularly to civil rights claimants such as Black people facing violence in the South. There was also a national movement away from the idea of Southern Reconstruction, Huq said.

WHEN HAS THE LAW BEEN USED?

While the statute is rarely used, a handful of lawsuits in recent years have cited it.

Notably, Trump was already facing a lawsuit that alleges he violated the KKK act when he attempted to overturn the election results of major cities last year.

The NAACP Legal Defense & Educational Fund filed the lawsuit in December, saying Trump disenfranchised voters of color by trying to "slow and stop vote counting efforts in tightly contested states."

Last year, the National Coalition on Black Civic Participation filed a federal lawsuit against right-wing political operatives Jack Burkman and Jacob Wohl, saying they violated the KKK act when they "conspired to intimidate and threaten many thousands of eligible voters."

Burkman and Wohl were accused of targeting Black voters in 85,000 robocalls that spread false information about voting by mail.

The statute was also cited last year ina lawsuit filed by St. Louis Circuit Attorney Kimberly M. Gardnerthat claimed a police union used a racially motivated conspiracy against her.

Gardner, a Black woman, said the police union harassed and intimidated her and city officials attempted to silence her and remove her from office. The lawsuit, which was ultimately dismissed, alleged that these were attempts to block her reform efforts.