The Democratic Party of US President-elect Joe Biden is on the verge of taking control of the Senate as results come in from two elections in Georgia.
Pastor Raphael Warnock is projected to win one seat. Fellow Democrat Jon Ossoff leads narrowly in the other.
If they both win, Biden will have a much better chance of pushing through his legislative agenda.
It comes as US lawmakers prepare to confirm Biden's presidential election victory.
A joint session of Congress will be held to count and confirm electoral college votes, but some Republicans are seeking to overturn the results in a number of states.
The bid is almost certain to fail. However, both houses of Congress may have to spend hours debating their objections.
And supporters of President Donald Trump are holding a "Save America Rally" in Washington DC. Trump is addressing them.
The mayor has asked for the National Guard to be deployed in the city amid fears of unrest.
Trump has refused to concede the 3 November election, repeatedly alleging fraud without providing evidence.
Why is there an election in Georgia?
The election is being rerun because of Georgia's rule that a candidate must take 50 percent of the vote in order to win.
None of the candidates in November's general election met that threshold.
With 98 percent of votes counted, US TV networks and the Associated Press news agency called the first of the two races for Warnock.
Control of the Senate in the first two years of Biden's term will be determined by the outcome of the second run-off.
Warnock is set to become the first black senator for the state of Georgia - a slavery state in the US Civil War - and only the 11th black senator in US history.
He serves as the reverend of the Atlanta church where assassinated civil rights leader Martin Luther King Jr grew up and preached.
Claiming victory, he paid tribute to his mother, Verlene, who as a teenager worked as a farm labourer.
"The other day - because this is America - the 82-year-old hands that used to pick somebody else's cotton went to the polls and picked her youngest son to be a United States senator," he said.
If both Democrats win, the Senate will be evenly split 50-50, allowing incoming Democratic Vice-President Kamala Harris the tie-breaking vote. The Democrats narrowly control the House of Representatives.
Ossoff has also claimed victory in his race against Republican Senator David Perdue, but that race is even tighter. At 33, he would be the Senate's youngest member for 40 years.
A Democrat has not won a Senate race in Georgia in 20 years but the party has been boosted by Biden's presidential election win over Trump there. Biden's margin of victory was about 12,000 votes among five million cast.
What is happening in Washington?
On Wednesday, more political drama will unfold in Washington DC as lawmakers gather in a special joint session to ratify the results of November's presidential election.
The typically procedural affair - which will affirm Biden's victory - has become unusually contentious, with about a dozen Republican senators vowing to challenge the results.
The group, led by Senator Ted Cruz, wants a 10-day delay to audit unsubstantiated claims of election fraud. The move is all but certain to fail as most senators are expected to endorse the results that have already been certified by US states.
Vice-President Mike Pence is set to preside over the session in his role as president of the Senate.
He has come under pressure this week from Trump to reject the certification, but the vice-president told Trump at their weekly lunch on Tuesday that he had no power in Congress to block Biden's win, according to the New York Times. Trump said the report was "fake news".
Biden is due to be inaugurated as president on 20 January. He won 306 votes to Trump's 232 in the US electoral college, which confirms the president.
Biden won at least seven million more votes than the president.
When will we get a result in Georgia?
Final results are expected later on Wednesday.
The margins are extremely tight. Warnock is projected to have won his race by 50.6 percent to 49.4 percent over incumbent Senator Kelly Loeffler.
Edison Research, which supplies election results to news organisations including the BBC, says Ossoff is leading by 50.2 percent, to 49.8 percent over Perdue.
More than 98 percent of ballots from Georgia's 159 counties have now been counted. The remaining votes come from the Atlanta suburbs, which are projected to go heavily for the Democrats.
More than three million voters - about 40 percent of those registered in Georgia - voted before Tuesday. Early voting benefited Biden in November's White House election.