Federal prosecutors have introduced a new twist in the Jan. 6 investigation by suggesting in a target letter that they could charge former President Donald J. Trump with violating a civil rights statute that dates back to the post-Civil War Reconstruction era, according to three people familiar with the matter.

The letter to Mr. Trump from the special counsel, Jack Smith, referred to three criminal statutes as part of the grand jury investigation into Mr. Trump’s efforts to reverse his 2020 election loss, according to two people with knowledge of its contents. Two of the statutes were familiar from the criminal referral by the House Jan. 6 committee and months of discussion by legal experts: conspiracy to defraud the government and obstruction of an official proceeding.

But the third criminal law cited in the letter was a surprise: Section 241 of Title 18 of the United States Code, which makes it a crime for people to “conspire to injure, oppress, threaten, or intimidate any person” in the “free exercise or enjoyment of any right or privilege secured to him by the Constitution or laws of the United States.”

Congress enacted that statute after the Civil War to provide a tool for federal agents to go after Southern whites, including Ku Klux Klan members, who engaged in terrorism to prevent formerly enslaved African Americans from voting. But in the modern era, it has been used more broadly, including in cases of voting fraud conspiracies.

A Justice Department spokesman declined to discuss the target letter and Mr. Smith’s theory for bringing the Section 241 statute into the Jan. 6 investigation. But the modern usage of the law raised the possibility that Mr. Trump, who baselessly declared the election he lost to have been rigged, could face prosecution on accusations of trying to rig the election himself.

A series of 20th-century cases upheld application of the law in cases involving alleged tampering with ballot boxes by casting false votes or falsely tabulating votes after the election was over, even if no specific voter could be considered the victim.

In a 1950 opinion by the Court of Appeals for the Sixth Circuit, for example, Judge Charles C. Simons wrote of applying Section 241 in a ballot box-stuffing case that the right to an honest count “is a right possessed by each voting elector, and to the extent that the importance of his vote is nullified, wholly or in part, he has been injured in the free exercise of a right or privilege secured to him by the laws and Constitution of the United States.”

In a 1974 Supreme Court opinion upholding the use of Section 241 to charge West Virginians who cast fake votes on a voting machine, Justice Thurgood Marshall cited Judge Simons and added that every voter “has a right under the Constitution to have his vote fairly counted, without its being distorted by fraudulently cast votes.”

The line of 20th-century cases raised the prospect that Mr. Smith and his team could be weighing using that law to cover efforts by Mr. Trump and his associates to flip the outcome of states he lost. Those efforts included the recorded phone conversation in which Mr. Trump tried to bully Georgia’s secretary of state to “find” enough additional votes to overcome Mr. Biden’s win in that state and promoting a plan to use so-called fake electors — self-appointed slates of pro-Trump electors from states won by Mr. Biden — to help block or delay congressional certification of Mr. Trump’s defeat.

“It seems like under 241 there’s at least a right to an honest counting of the votes,” said Norman Eisen, who worked for the House Judiciary Committee during Mr. Trump’s first impeachment. “Submitting an alternate electoral certificate to Congress (as opposed to casting false votes or counting wrong) is a novel scenario, but it seems like it would violate this right.”

The prospect of charging Mr. Trump under the other two statutes cited in the target letter is less novel, if not without hurdles. Among other things, in its final report last year, the House committee that investigated the events that culminated in the Jan. 6 attack on the Capitol had recommended that the Justice Department charge the former president under both of them.

One, Section 371 of Title 18, makes it a crime to conspire to defraud the United States. The other, Section 1512, includes a provision that makes it a crime to corruptly obstruct an official proceeding.

A spokesman for Mr. Trump declined requests to clarify what was in the letter.

Citing the statutes in the letter, which Mr. Trump has said he received on Sunday, does not necessarily mean that any charges brought by Mr. Smith would have to be based on them. But the letter’s contents provide a road map to investigators’ thinking.

The conspiracy to defraud the United States statute, if used, raises the question of who Mr. Trump’s co-conspirators would be.

Some of those who worked most closely with Mr. Trump in promoting the lie that Mr. Trump had been robbed of a victory by widespread fraud, including lawyers like Rudolph W. Giuliani and John Eastman, had not received target letters, their lawyers said on Tuesday.

The corrupt obstruction of a proceeding charge has been used against hundreds of Jan. 6 rioters and has served as the Justice Department’s go-to count in describing the central event that day: the disruption of the Electoral College certification process that was taking place inside the Capitol during a joint session of Congress.

The law was originally passed as part of the Sarbanes-Oxley Act, a measure meant to curb corporate malfeasance. Defense lawyers for several rioters have challenged its use against their client, saying it was meant to stop crimes like witness tampering or document destruction and had been unfairly stretched to include the chaos at the Capitol.

But in April, a federal appeals court upheld the viability of applying that charge to participants in the Capitol attack. Still, unlike ordinary rioters, Mr. Trump did not physically participate in the storming of the Capitol, although he had summoned supporters to Washington that day and railed about the unwillingness of Vice President Mike Pence, who was presiding over the proceedings in Congress, to stop them.

A second attempt to invalidate the obstruction count in the federal appeals court in Washington has focused specifically on a provision of the law dictating that defendants must act “corruptly” in committing the obstructive act.

Defense lawyers have argued that this provision does not apply to many ordinary Jan. 6 rioters who did not act corruptly because they stood to gain nothing personally by entering the Capitol. It could, however, be applied more easily to Mr. Trump, who stood to gain an election victory by obstructing the certification process.

William K. Rashbaum and Glenn Thrush contributed reporting.