PHOENIX — Democrats padded their narrow leads in key Arizona contests on Thursday, but the races for Senate and governor were still too early to call with about a fifth of the total ballots left to be counted.

The Democratic incumbent, Senator Kelly led Republican challenger Blake Masters by 5.6 percentage points, while Democrat Katie Hobbs had a much tighter lead of 1.4 points against Republican Kari Lake in the governor’s race. Democrats also led in the races for secretary of state and attorney general.

Election officials in Maricopa County, which includes metro Phoenix and more than 60 percent of voters, expected to begin reporting results Friday from a crucial group of ballots — nearly 300,000 mail ballots that were returned on Election Day. That group has swung wildly in recent election cycles, from strongly Democratic in the 2018 midterms to strongly Republican in 2020.

The races will hinge on whether those late-counted ballots look more like 2018 or 2020.

The answer will determine who wins extremely tight races for Senate and House, as well as governor, secretary of state and attorney general. At stake are control of Congress and the rules for the 2024 presidential election in a crucial battleground state.

In the House, the three-term Democratic Representative, Tom O’Halleran, lost his race Thursday to Republican Eli Crane, a businessman and former Navy SEAL, after his rural district was redrawn to become significantly more conservative. Democrats had hoped Mr. O’Halleran’s long history in the area and his background as a retired police officer could help him survive.

President Trump’s claims about the 2020 election have rejiggered voting patterns across the country and especially in Arizona, which has played a starring role in  theories suggesting the outcome was tainted. That makes it even more complicated for news organizations to declare winners because historical data doesn’t necessarily apply.

It could take several days before it’s clear who won some of the closer contests, as was the case in the 2018 and 2020 elections. About 500,000 ballots remained uncounted, most of them in metro Phoenix and Tucson.

Maricopa County officials emphasized that this year’s process was no different than in previous years.

“This is how things work in Arizona and have for decades,” said the Republican chairman of the county board of supervisors, Bill Gates. He said staff are working 14 to 18 hours a day and will continue through the weekend.

“We are doing what we can and still maintaining accuracy,” Mr. Gates said.

Protracted vote counts have for years been a staple of elections in Arizona, where the overwhelming majority of people vote with mail ballots and many wait until the last minute to return them. But as Arizona has morphed from a GOP stronghold to a competitive battleground, the delays have increasingly become a source of national anxiety for partisans on both sides.

Processing mail ballots is time-consuming because officials have to verify that the voters didn’t vote in person and that the signatures on their ballot envelopes match those on file. Maricopa County officials said they received a record number of mail ballots returned on Election Day.

With Republicans still in the hunt, it remained unclear whether the stronger-than-expected showing for Democrats in much of America would extend to Arizona.

Republicans were antsy for more results, believing the remaining ballots strongly favor them.

The GOP nominated a slate of candidates who earned Mr. Trump’s endorsement after claiming his loss to President Biden was tainted. Ms. Lake claimed Thursday morning that Maricopa County officials are “slow rolling” the release of results to make it look like Democrats are doing better than they actually are.

“We’re going to win this and there’s not a darn thing they can do about it, but they’re trying to pour cold water on this movement,” Ms. Lake told conservative radio host Charlie Kirk. “This movement is on fire, and no amount of water is going to put that fire out. We the people are taking our government back.”

Gates pushed back on Ms. Lake’s accusations of a purposely slow count and said ballots were counted in the order in which they came in.

“We are absolutely not slow rolling it,” he said. “And if their team had been paying attention before the election, they would’ve heard us talking about this over and over again, that we were not going to have results on election night, that it would take days.”

Ms. Lake has pledged to immediately call lawmakers into special session upon being sworn in to make massive changes to Arizona election laws. She wants to significantly reduce early and mail voting, options chosen by at least 8 in 10 Arizona voters, and to count all ballots by hand, which election administrators say would be extremely time consuming.

“This election will be determined by the voters, not by the volume at which an unhinged former television reporter can shout conspiracy theories,” Ms. Hobbs wrote on Twitter.

Officials in Maricopa County said they were able to count 17,000 ballots cast in person on Election Day that were affected by a printing mishap. The printer problem at 70 of 223 vote centers prevented on-site vote-counters from reading those ballots, a problem that slowed voting in some locations and infuriated Republicans who were counting on strong Election Day turnout.

Republicans who control the three-member board of supervisors in southeastern Arizona’s GOP-heavy Cochise County cited the problem in Maricopa County as they urged the state Supreme Court to let them hand-count all the ballots cast in the election. They’re appealing a decision that blocked them from going beyond the traditional hand-count of a small sample of ballots, which is meant to test the accuracy of tabulation machines.

Election and technology experts note that the machines are tested, certified and retested and are not only faster but much more accurate than counting by hand, which can be prone to errors.