Democrat Sherrod Brown asked Republican Dan Sullivan to put on his mask while speaking in the chamber.
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North America technology reporter
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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.
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BBC News, Washington
The California senator is the first female, first black and first Asian-American US vice-president-elect.
After days of waiting, US networks reacted to Joe Biden being victor in Pennsylvania and therefore winning the election.
It is third time lucky for Democrat Joe Biden, who has won the race to become the US president.
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Democratic presidential candidate Joe Biden urges Americans to come together after the election.
President Trump’s unfounded declaration that "frankly, we did win this election" has prompted a strong reaction from Democratic politicians.
Congresswoman Alexandria Ocasio-Cortez, who is projected to win re-election in New York, condemned Trump’s claim as “illegitimate, dangerous, and authoritarian”.
“Count the votes. Respect the results,” she tweeted.
House Representative for Minnesota Ilhan Omar called Trump a “dangerous man”, tweeting “you can’t stop ballots from being counted”.
“This isn’t a dictatorship,” she added.
Amy Klobuchar, the senator for Minnesota, struck a more measured tone.
“All votes must be counted. We live in a democracy,” she wrote minutes after Trump's statement.
California Democrat Nancy Pelosi is singing the praises of House Democrats, who have retained their majority in the chamber.
It means Pelosi will likely return as Speaker of the House when the new Congress convenes.
The issue that helped hand Democrats the win was healthcare, Pelosi said.
Democrats still need to win four seats in the upper chamber of Congress, the Senate, to gain a majority there.
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"We knew this was going to go long, but who knew we would go into maybe tomorrow morning, maybe even longer!" Biden says, speaking now from Delaware.
"But we feel good about where we are. I'm here to tell you tonight we believe we're on track to win this election."
He adds: "It ain't over until every vote, every ballot is counted."
Watch his speech here...
Former Nasa astronaut Mark Kelly has just been on stage in Tucson, Arizona, declaring a victory over Republican senator and former Air Force officer Martha McSally.
"The votes are counted, and we're going to be successful in this mission," he said on stage. Fox News projected his win.
"Tonight is not about celebrating," he added. "Tonight is about getting to work."
In a message to his daughters, he said that when they were young he used to go to work blasting off into space. But this time, it's to Washington DC where he'll be journeying into the great unknown.
Kelly is a political newcomer whose wife, Gabrielle Giffords, is a former congresswoman who was shot in the head while meeting with constituents in 2011. In the years that followed, the couple became well-known for their advocacy on gun control.