With control of the Senate hanging in the balance, two runoff contests in Georgia remained too close to call early Wednesday as the advantage seesawed back and forth after election officials had tallied more than 4.2 million votes.

The races feature two Republican candidates — Senator Kelly Loeffler and David Perdue, whose Senate term ended on Sunday — trying to fend off their Democratic challengers, Jon Ossoff and the Rev. Raphael Warnock, in contests that have drawn national attention and unprecedented levels of campaign spending.

Democrats saw some significant signs for optimism. Both Senate candidates were winning a larger share of the vote in county after county than President-elect Joseph R. Biden Jr. won in November, when he narrowly carried the state.

Mr. Warnock was running slightly stronger in his race against Ms. Loeffler than Mr. Ossoff was in his contest with Mr. Perdue. After a large tranche of votes in DeKalb County were reported after 11 p.m., many Democrats began to cautiously cheer the possibility of victory.

“With new votes joining the tally, we are on a strong path,” wrote Stacey Abrams, the Democratic activist and former candidate for Georgia, on Twitter.

About 95 percent of voters in both runoff races said that determining control of the Senate was a “major factor” in their vote, according to A.P. voter surveys, with about three in five calling it “the single most important factor.”

Mr. Biden and President Trump both campaigned in the state on Monday, a sign of the high stakes of the races. If either Republican candidate wins, Senator Mitch McConnell, Republican of Kentucky, will remain the majority leader. But if both Democrats win on Tuesday, the party will gain control of the chamber, with Vice President-elect Kamala Harris serving as the tiebreaking vote.

“This could be the most important vote you will ever cast for the rest of your life,” Mr. Trump said at his rally on Monday. The races are the final elections during his presidency, and Mr. Trump, as usual, loomed large.

A majority of voters, 56 percent, said they disapproved of how Mr. Trump has handled the results of the 2020 presidential election, which he lost but has sought to overturn and undermine. At the same time, voters approved of how Secretary of State Brad Raffensperger of Georgia, whom Mr. Trump has sparred with, has handled the situation.

Mr. Biden narrowly carried Georgia in November, becoming the first Democratic presidential candidate to do so since 1992.

But he did not pull ahead of Mr. Trump in the vote counting in Georgia until days after the election. If the Senate races remain tight on Tuesday, the counting — and a final result — would drag later into the week, as it did in the general election in November.

Mr. Biden’s victory in Georgia has lifted the party’s hopes before the runoffs. But Democrats did not fare as well down ballot in November. Mr. Perdue far outpaced Mr. Ossoff by nearly 90,000 votes in their first matchup, suggesting that Democrats still have to make up ground to win the runoff.

The racial makeup of the final electorate will be crucial in a state where Black voters overwhelmingly support Democrats and white voters back Republicans. According to data compiled by georgiavotes.com, Black voters made up a larger share of early voters for the runoff — nearly 31 percent — than they did in the general election, when it was closer to 28 percent.

Mr. Warnock, who is the pastor of Ebenezer Baptist Church in Atlanta, the spiritual home of the Rev. Dr. Martin Luther King Jr., is seeking to become the first Black Democrat elected to the Senate from the South. He and Mr. Ossoff, a 33-year-old documentary film executive, ran in tandem throughout the runoffs.

Mr. Perdue, the former chief executive of Dollar General, and Ms. Loeffler, who was appointed to the Senate a year ago and is seeking a full term, have cast the race as a necessary check on Democratic power in Washington in 2021, though these efforts have been complicated by Mr. Trump’s continued insistence, without evidence, that he won re-election.