While trailing her opponent by roughly 35,000 votes, Loeffler delivered remarks in the early hours of Wednesday morning projecting confidence in her race and insisting she still had a path to victory.

"This is a game of inches. We're going to win this election," Loeffler told a crowd of supporters in Buckhead.

"I'm not going to stop working. In the morning, in fact, I'm going to be heading to Washington, D.C., to keep fighting. We're going to keep fighting for this president," Loeffler said, teasing the counting of the Electoral College vote in Congress on Wednesday, which nearly a dozen GOP senators plan to object to.

Her opponent, Warnock, began speaking moments after she finished. Warnock and Ossoff did not hold large watch parties due to COVID-19 concerns.

While Loeffler and Perdue have carried the lead in the Senate races for most of the night, with the bulk of votes in DeKalb County coming in, Warnock is leading Loeffler statewide, and Ossoff is close behind Perdue.

In DeKalb County, a Democratic stronghold where a massive amount of votes came in, Ossoff currently leads 82.5% to Perdue’s 17.5%. Warnock leads 83.2% to Loeffler’s 16.8%.

"Now you may be asking why is Warnock not doing much better than Ossoff?" said ABC News Chief National Affairs Correspondent Tom Llamas. "If you essentially come out and you look at all the counties that surround Atlanta, Warnock is over-performing Ossoff by about 2,000 votes so far in each of those counties."

According to the secretary of state’s website hosting the unofficial election results, there were at least 1,231,662 votes cast on Tuesday that have been counted so far -- a high turnout for runoff elections.

-ABC News' Meg Cunningham, Kendall Karson and Quinn Scanlan

Former Georgia gubernatorial candidate Stacey Abrams, and founder of Fair Fight, sent an encouraging tweet to supporters moments after Warnock took the lead over Loeffler in his Senate race with 95% of the expected vote reporting in.

“With new votes joining the tally, we are on a strong path. But even while we wait for more, let’s celebrate the extraordinary organizers, volunteers, canvassers & tireless groups that haven’t stopped going since Nov. Across our state, we roared. A few miles to go...but well done!” Abrams tweeted.

Gabriel Sterling, the state voting system implementation manager, said at an earlier election update that the largest portion of remaining uncounted votes was out of DeKalb County, a heavily Democratic suburban Atlanta area.

Gabriel Sterling, the state voting system implementation manager, said in an evening election update that the largest portion of remaining uncounted votes is from DeKalb County, a heavily Democratic suburban Atlanta area.

"The biggest tranche of votes that exists out there in a single bucket right now still looks to be the advanced voting in DeKalb County," Sterling said.

With 80% of the expected vote reporting in, GOP candidates Perdue and Loeffler are leading their races by small margins.

Sterling said from the press conference in Atlanta that he wasn't aware of any issues that could delay the reporting but added, "It can be like seesaw for the rest of the evening."

Sterling said 64 of the state's 159 counties have completed reporting all votes.

-ABC News' Quinn Scanlan

Warnock called his projected victory a "historic moment," saying he "can't wait" to be in the upper chamber of Congress "to represent the concerns of ordinary people."

"I'm deeply honored that the people of Georgia decided to place their faith in me and have decided to send me to represent their interests in Washington, D.C.," Warnock told ABC News Chief Anchor George Stephanopoulos in an interview Wednesday on "Good Morning America."

"Certainly, this is a historic moment and I'm just deeply grateful to be a vessel in a moment in which we're facing such large problems in our country," he added, "and I can't wait to get to the U.S. Senate to represent the concerns of ordinary people."

Warnock, a senior pastor of the Ebenezer Baptist Church in Atlanta, the former pulpit of the Rev. Martin Luther King Jr., is the first Black senator Georgia has elected and only the 11th Black senator elected in U.S. history.

"Georgia is in such an incredible place when you think about the arc of our history, we are sending an African-American pastor of Ebenezer Baptist church where Martin Luther King Jr. served," he said. "This is the reversal of the old southern strategy that sought to divide people. In this moment we've got to bring people together in order to do the hard work and I look forward to doing that."

When asked about his top priority for this year in the Senate, Warnock said -- as he has throughout his campaign -- that the country needs to get the coronavirus pandemic under control.

"Like so many Americans, as we witnessed the incredible death toll over 350,000 Americans lost lives, lost livelihoods, we need a national strategy that takes this virus seriously, that gets the vaccine distributed safely and efficiently," he said. "We've got to re-open our economy, get our kids safely back to school and we got to make sure that people know that they will have their health care, particularly in the middle of a pandemic."

-ABC News' Quinn Scanlan