In a fiery statement, Gabriel Sterling, a Republican, said: “It’s all gone too far! All of it! It has to stop!”
Georgia is carrying out a second recount of votes in the state at the Trump campaign’s request.
Democratic president-elect Joe Biden was declared the narrow winner there.
Trump campaign spokesman Tim Murtaugh said they are trying to make sure “that all legal votes are counted and all illegal votes are not”.
“No-one should engage in threats or violence, and if that has happened, we condemn that fully.”
It came after US Attorney General William Barr said his justice department has so far found no proof to back Mr Trump’s claims of fraud in the election.
Who has been threatened?
Voice quaking with anger at a news conference in Atlanta, Mr Sterling, the state’s voting systems implementation manager, rebuked his fellow Republicans, including the president.
He said a 20-year-old contractor in Gwinnett County for Dominion Voting Systems, which has become the subject of baseless right-wing conspiracy theories, had received death threats. The worker’s family was also getting harassed, Mr Sterling added.
The unnamed man had been threatened with a noose and accused of treason, Mr Sterling said, after transferring a report on ballot batches to a county computer so he could read it.
Mr Sterling said he himself has a police guard outside his home, while the wife of Georgia’s Secretary of State, Brad Raffensperger, was “getting sexualised threats through her cell phone”.
“Mr President, you have not condemned these actions or this language,” added Mr Sterling. “Senators, you have not condemned these actions or this language.
“We need you to step up and if you’re going to take a position of leadership, show some!”
He added: “Death threats, physical threats, intimidation, it’s too much, it’s not right, they’ve lost the moral high ground to claim that it is.”
Mr Sterling also cited threats of violence against Chris Krebs, who was fired last month as head of the US Cybersecurity and Infrastructure Security Agency after he disputed Mr Trump’s fraud claims.
Mr Sterling condemned Trump lawyer Joe DiGenova, who said on Monday that Mr Krebs should be “taken out at dawn and shot”.
Addressing Mr Trump directly, Mr Sterling continued: “You have the right to go to the courts. What you don’t have the ability to do, and you need to step up and say this, is stop inspiring people to commit potential acts of violence.
“Someone’s going to get hurt, someone’s going to get shot, someone’s going to get killed, and it’s not right.”
He added: “Be the bigger man here, and stop, step in, tell your supporters, don’t be violent, don’t intimidate. All that’s wrong, it’s un-American.”
How has Trump reacted?
President Trump responded by retweeting a video of Mr Sterling’s speech, but without referencing the concerns over threats of violence.
— Donald J. Trump (@realDonaldTrump) December 2, 2020
Before and since, he has fired off many more tweets on the same subject, all without credible evidence.
He shared a conspiracy theory about voting machines in Georgia, claimed Mr Biden’s win in Arizona was “impossible”, the results in Nevada were “fake” and also claimed without proof: “We won Michigan by a lot!”
What’s the latest with the Trump election challenge?
On Tuesday, the president’s campaign filed a lawsuit with Wisconsin’s supreme court challenging the state’s presidential vote results.
The petition came a day after Mr Biden was certified as the winner in the Midwestern state by about 20,000 votes.
The Trump legal action challenges more than 220,000 ballots in Wisconsin based largely on technicalities.
It alleges clerks filled out missing information on postal ballots and objects to an event where election officials collected and checked votes in a park in the city of Madison, rather than polling stations.
Mr Trump and his allies have failed to make significant headway in their efforts to challenge the results in Arizona, Pennsylvania, Georgia, Michigan and Nevada.
His attorney general, William Barr, said on Tuesday that the justice department so far had “not seen fraud on a scale that could have effected a different outcome in the election”.
The comments were seen as a big blow to Mr Trump, as Mr Barr is a close ally.
A DOJ spokesperson later stressed the department had not concluded its investigation.