Georgia election official says Trump will be responsible for any violence resulting from unsubstantiated election fraud claims.
Georgia election official Gabriel Sterling calls for an end to threats of violence against staff.
Democrat Sherrod Brown asked Republican Dan Sullivan to put on his mask while speaking in the chamber.
By Sam Cabral
BBC News, Washington
By Lucy Rodgers
BBC Visual Journalism team
Democratic Senator Chris Coons says Republicans will support Joe Biden's transition government if the basis for legal challenges is not shown.
By Marianna Brady, Sam Cabral and Silvia Martelli
BBC News, Washington
From transgender State Senator Sarah McBride to 25-year-old Madison Cawthorn - here are some of the new faces making history in US politics.
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Pennsylvania Republican Senator Pat Toomey is among several critics from the president's own party who are disputing details from his news conference at the White House yesterday.
"I saw the president's speech last night and it was very hard to watch," he told NBC earlier today.
"The president's allegations of large-scale fraud and theft of the election are just not substantiated. I'm not aware of any significant wrongdoing here."
"Look, there are irregularities in every election. They tend to typically be very small and involve just a handful of ballots."
Toomey, who is due to retire in 2022, also said he had no idea how long it would take for votes to be fully counted in Pennsylvania, a state leaning towards Biden at present.
"It's going to take the time that it takes," he said, adding that the remaining votes will likely be for Democrats. "But at this point we just don't know. That's why we go through the process - to find out."
Donald Trump's two sons have rebuked Republicans for failing to back the president as he struggles to win re-election.
Trump's eldest son, Don Jr, accused the party of being "weak". His brother Eric warned: "Our voters will never forget you if your [sic] sheep!"
Senior Republicans such as Utah Senator Mitt Romney and Maryland Governor Larry Hogan have warned the Trump campaign against undermining the democratic process.
Don Jr took to Twitter to dish out his ire for those who may be eyeing up a presidential run in 2024.
"The total lack of action from virtually all of the '2024 GOP [Republican] hopefuls' is pretty amazing," he wrote.
"They have a perfect platform to show that they're willing & able to fight but they will cower to the media mob instead. Don't worry @realDonaldTrump will fight & they can watch as usual!"
The younger Trump later told supporters in Atlanta, Georgia - one of the key battleground states where votes are still being counted - that his father was right to mount legal challenges to the vote-counting process.
"I think the number one thing that Donald Trump can do in this election is fight each and every one of these battles to the death," he said.
Republican Randi Reed clashes with Emily Maitlis over her claims about vote counts being stopped.
Donald Trump has declared an unsupported victory in a speech from the ceremonial East Room of the White House - with millions of ballots yet to be counted.
Several top Republicans and conservative commentators are expressing alarm at Trump's unsubstantiated comments.
Speaking on ABC News, former New Jersey Governor and Trump adviser Chris Christie called the president's speech the wrong move - both strategically, and as president.
"It's a bad strategic decision," he said. "It's a bad political decision."
Rick Santorum, former Republican Senator from Pennsylvania, said he was "very distressed" by Trump's comments. "Using the word fraud... I think is wrong," he said on CNN.
And Ben Shapiro, a conservative commentator and critic of Trump, tweeted calling the comments "deeply irresponsible".
Republican Senator Lindsay Graham holds his seat in South Carolina and predicts a Donald Trump win.
Excitement is building among Republicans in our voter panel text group as Florida looks good for Trump.
Jim (R - Indiana) : “Are you seeing this? Trump is winning urban areas in Florida +4% and Hispanics +13%".
Gavin (R - Georgia): “Trump is going to win FL and NC! Feeling great at this moment!”
Eliana Girard (R - Florida): “We’re watching at Club 45 party with 500 people.”Copyright: BBC