Election officials in several closely contested states said they are worried about the safety of their workers amid threats and gatherings of angry protesters outside vote tabulation centers, drawn by President Donald Trump's baseless claim of widespread fraud in the race for the White House.

"I can tell you that my wife and my mother are very concerned for me," said Joe Gloria, the registrar in Clark County, Nevada, which includes Las Vegas. He said his staff was bolstering security and tracking vehicles coming and going from the election offices.

But he added that he and others would not be stopped from “doing what our duty is and counting ballots".

Groups of Trump supporters gathered at vote tabulation sites in Detroit and Philadelphia again Friday, decrying counts that showed Democrat Joe Biden leading in those and other key states.

While the protests have not been violent or very large, local officials were distressed by the gatherings and concerned about the relentless accusations.

Michigan Attorney General Dana Nessel tweeted a plea Thursday to stop making harassing and threatening calls to her staff.

"Asking them to shove sharpies in uncomfortable places is never appropriate & is a sad commentary on the state of our nation," wrote Nessel, a Democrat, referring to a false conspiracy theory that Trump supporters were told to fill out ballots with Sharpie markers instead of regular pens so that their votes wouldn't be counted by the machines.

Dozens of Trump supporters rallied outside Detroit's convention centre on Friday morning, where election workers have counted ballots.

"Stop the steal," the protesters chanted. Some carried signs that read, "Make Elections Fair Again", and "We Love Trump". Police cordoned off streets leading to the tabulation centre and maintained a close watch on the protest.

Arizona Secretary of State Katie Hobbs, speaking on CNN, said her main concern was staff safety but that sheriff's deputies were providing protection. She said the protesters were causing delay and disruption and preventing those employees from doing their job.

On Thursday, about 100 Trump supporters gathered in front of the Maricopa County election centre in Phoenix, some carrying military-style rifles and handguns. Arizona law allows people to openly carry guns.

Authorities at the centre used fences to create a freedom of speech zone and keep the entrance to the building open. The crowd took turns chanting "Count the votes!” and "Four more years!” and complaining through a megaphone about the voting process.

They paused to listen as Trump spoke from the White House, where he repeated many of his groundless assertions of a rigged vote.

They whooped and clapped when the president said, "We're on track to win Arizona." The Associated Press has called Arizona for Biden.

In Atlanta, roughly 100 chanting Trump supporters gathered outside State Farm Arena Thursday as votes were being counted. Several Atlanta police officers monitored the scene.

Tom Haas, 50, who said he was visiting Atlanta from Chicago on business, said he was convinced Trump had won the election. "There's obvious voter fraud, and it's coming out of the larger Democratic-run cities," he said. "Atlanta is one of them."

"Our democracy is under attack,” he said, echoing Trump's language. “We're losing America because we're losing a fair election for the nation."

In Las Vegas, about 100 backers of the president chanted as they stood along the road in front of the election offices.

Meanwhile, Facebook banned a large group called Stop the Steal that Trump supporters were using to organise protests against the vote count. Some members had called for violence, while many falsely claimed Democrats are stealing the election. The group had amassed more than 350,000 members before Facebook took it down.