Former President Barack Obama tweeted to Georgia voters that while state polls close at 7 p.m., they should stay in line if they've arrived at their polling location in time.

"You have the right to vote, no matter how long it takes," Obama tweeted.

Some precincts in the state will be open past 7 p.m. due to court orders.

Obama joined a virtual rally for Democratic candidates Rev. Raphael Warnock and Jon Ossoff earlier this month and has appeared in digital ads for both candidates. On Monday, the former president tweeted "the stakes could not be higher" in promoting the runoff elections.

A majority of voters in Georgia's Senate runoffs think the presidential election was fair, preliminary exit poll results show.

More than half -- 56% -- of voters think the presidential election in Georgia was conducted fairly, while 41% do not, according to the preliminary results.

President-elect Joe Biden defeated President Donald Trump by nearly 12,000 votes in Georgia. Trump repeatedly has made unsubstantiated claims of voter fraud in Georgia, among other states.

Most voters also express at least some confidence in the current runoff elections. Seventy-three percent are very or somewhat confident that votes in the runoffs will be counted accurately, while 26% are not very or not at all confident, according to the preliminary results. This is down from a similar question in November, when 85% were very or somewhat confident that votes in their state would be counted accurately.

-ABC News' Gary Langer, Christine Filer and Steven Sparks

Gabriel Sterling, the voting system implementation manager in Georgia Secretary of State Brad Raffensperger's office, provided an update on the runoff elections, reporting no major issues at this point in the day.

"The biggest thing is we have to deal with is rumors," Sterling said. "Everybody's kind of on edge for some of these things. But in general, it's been steady as she goes."

Sterling said that while there are also reports circulating about turnout, it's impossible for the state to know how many have voted so far Tuesday because the voting systems are not connected to the internet.

"So it's anecdotal evidence that we receive," he said. "If there's not lines, it doesn't mean that there's not a high turnout. It just means they're processing people."

Sterling predicted Tuesday's turnout could be as low as 600,000 or as high as 1.1 million, stressing, "We just have no way of knowing."

The maximum number of absentee ballots outstanding, he said, is 306,855. Sterling later tweeted a correction to the maximum number of potential outstanding absentee ballots, saying the correct number is 229,357. These are due by 7 p.m. when most polls close across the state.

Sterling said the public will know about the biggest bulk of votes Tuesday night, but it's unclear when final results will be known.

"We're gonna start getting results tonight. We're gonna get the biggest bulk of them, like we did last time, it depends on the margin," he said. "If I'm a betting person, which I'm not, I would say it's gonna be a couple of days, because I anticipate it will be a close race one way or the other."

-ABC News' Quinn Scanlan

Turnout among partisan groups is central to the outcome of the two runoff races in Georgia. In addition to Black and other racial and ethnic minority voters, another group to watch is evangelical white Christians, core Republicans.

Black voters appeared to hold on to their share of the state's electorate, according to preliminary exit poll results.

Black people -- a core Democratic group -- account for 29% of voters in these preliminary results, compared with 28% in November.

Evangelical white Christians account for 34% of runoff voters preliminarily, about the same as in November.

In purely partisan terms, Republicans outnumber Democrats by three points in these preliminary results, 39% to 36%.

-ABC News' Gary Langer, Christine Filer and Steven Sparks

Up by roughly 35,000 votes statewide, Warnock declared victory in Georgia with a virtual speech to supporters in the early hours of Wednesday morning.

"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,” Warnock said.

ABC News has not made a projection on the race, but if Warnock wins, the native-born son, who delivers sermons from the pulpit that once belonged to the Rev. Dr. Martin Luther King Jr., will become the first Black senator from Georgia.

“So I come before you tonight as a man who knows that the improbable journey that led me to this place in the historic moment in America could only happen here,” Warnock continued. “May my story be an inspiration to some young person who is trying to grasp and grab hold of the American dream.”

Taking a page from President-elect Joe Biden's playbook, Warnock went on to say he'd be a senator for those who didn't vote for him as much as for those who did support him.

“To everyone out there struggling today, whether you voted for me or not, know this, I hear you, I see you. And every day I'm in the United States Senate, I will fight for you,” he said.