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

On Tuesday, nearly a third of polling locations throughout Maricopa County — home to Phoenix and more than 60 percent of the state’s voters — had problems with the printers that produce ballots on demand for individual voters. Starting early Tuesday morning, printers at 70 of the county’s 223 polling sites produced ballots with ink that was too light to be properly read by vote-counting machines, causing the ballots to be rejected, according to county officials. These officials had previously said that a smaller number of sites had problems.

The officials said they had yet to determine the cause of the printer problems; they said the printers passed required logic and accuracy tests ahead of Tuesday and had been used during the August primary election and the 2020 elections with the same settings, with no problems.

Voters had the options of waiting for the problems to be fixed, going to different polling locations, or dropping their ballots into secure boxes that were transferred to downtown Phoenix and counted there. Voters placed about 17,000 ballots in the secure boxes, a higher number than in previous elections, county officials said. They said all votes will be counted, that all voters who wanted to cast a ballot were allowed to do so and that the printer problems will not affect the counting of votes.

Maricopa’s problems remained a mystery Thursday to officials in Washington, who have been disappointed since Election Day by the lack of a clear explanation communicated to both voters and the agencies charged with election oversight, said two people tracking the developments. They spoke on the condition of anonymity because they were not authorized to speak to the press.

Kari Lake wants to upend how Arizonans vote, how their votes are counted

In a state central to widespread conspiracy theories after President Donald Trump’s loss in 2020, some Republicans leveraged the problems in Maricopa County to call for elimination of early voting and machines that count votes. Though early voting has long been popular in Arizona, ballots returned in the days leading up to Election Day and on Election Day, always take time to process, and ballots are processed in the order they are received. To post results more quickly, county leaders for weeks urged voters to return their ballots — which had more races than ever before — as quickly as possible.

Election workers were working through about 400,000 ballots in Maricopa County as of Thursday night. Officials here said they always expected the count to take as many as 12 days, though they had expected to report at least 95 percent of results by Friday. On Thursday, county officials said that it would take longer to meet that goal and that they are working through the Veterans Day federal holiday and the weekend.

Voters dropped off about 290,000 ballots on Election Day, the highest number ever released. The high volume of late drop-offs suggests many voters may have acted on instructions from Republican leaders and candidates who urged people to either vote in person or hand-deliver early ballots at polling locations.

Some Republicans claimed, without evidence, that the drip-drip release of results — which happens during every election here — suggested county officials wanted to delay what they asserted would be a win by Lake, and perhaps other Republican candidates.

Officials in Pima County, home to Tucson, swatted away such allegations. Gabriella Cázares-Kelly, the county recorder, said it was taking time to process the high volume of early ballots that didn’t arrive until Election Day. “We are following the law,” she said.

Maricopa County Supervisor Bill Gates (R) noted that it routinely takes days to complete tabulation in the county, a pattern that has recently drawn national attention because of Arizona’s swing-state status and the tight margins in statewide contests. Gates, who twice ran the state GOP’s Election Day integrity efforts, said Lake might not be familiar with the county’s tabulation process.

“Quite frankly, it is offensive for Kari Lake to say these people behind me are slow rolling when they’re working 14 to 18 hours,” he said, gripping a lectern at times during a 45-minute news conference. “I really hope this is the end of that now. We can be patient and respect the results.”

Gates said it is important that Arizonans don’t think “that we’re picking and choosing which ballots to tabulate. We use an accounting concept: first in, first out.”

Researchers examining attempts on social media to delegitimize election results said fraud narratives had gotten less traction in the immediate aftermath of the vote. But others warned that a prolonged count in Arizona could create an opportunity for misleading narratives to take hold or for rogue actors to try to disrupt the process.

Most immediately, Republican candidates and their allies in Arizona seized on the mechanical issues to prime the public for sweeping legislative changes. Lake ran on a platform during the primary election to count millions of votes not by machines, but by hand, a method that election experts say is less accurate. She favors “one-day voting,” where ballots are cast in assigned precincts. Arizona allows people to vote by mail, and in Maricopa County, they can vote at any voting location.

Lake was notably vaguer in the final days of campaigning about her plans for electoral reform.

At a stop southeast of Phoenix on the Sunday before Election Day, she told reporters simply that she planned to “work with our wonderful lawmakers, and we’ll come up with great laws that secure the vote.”

Her most hard-line allies also seemed to be equivocating. Wendy Rogers, a far-right state senator who has pushed for “decertification” of the 2020 election, a process that experts say is not possible under state or federal law, refused to commit to a system that would only allow voting on a single day — an idea that has been pushed by far-right activists here. When asked at the same event whether she favored such a proposal, she replied, “Essentially.”

But the problems in Maricopa County gave Lake and her supporters a fresh target for their ire. In an appearance on a radio show hosted by Charlie Kirk, the founder and president of Phoenix-based Turning Point USA, Lake called for a “task force to investigate what went wrong, how these anomalies happened.”

“That’s either maladministration, incompetency, we don’t know what it is,” she added.

Kirk went further, arguing without evidence, “I believe it was a traffic jam by design.”

How a pro-Trump youth group remade the Arizona GOP, testing democracy

But that belief wasn’t echoed by Lake, who had a delicate dance to pull off — railing against the administration of an election that, she told her supporters, will place her in the governor’s office.

“It’s a messed-up election system,” she said. “We knew we had to trudge through it to get to victory.”

That message left fellow Republican candidates in a difficult position. Other campaigns took their cues from Lake about how to respond to the uncertainty in the days after the election, according to a Republican familiar with the discussions. Blake Masters, the Republican nominee for U.S. Senate in Arizona, suggested on Tuesday that something nefarious was occurring, but he fell mostly silent on social media as Sen. Mark Kelly (D-Ariz.) gained an edge over him in incomplete results.

A fundraising appeal from Masters’s campaign on Thursday did not allege impropriety but argued that “some of the issues we’ve see occur during this election are troubling.” It added, “We’re expecting a contested road forward and legal battles to come.”

Abraham Hamadeh, the Republican nominee for attorney general, attacked Maricopa County but did not argue that the vote, which was showing him neck-and-neck with Democrat Kris Mayes, was fraudulent.

The exception was Mark Finchem, the GOP candidate for secretary of state, who was trailing Democrat Adrian Fontes in preliminary results. Finchem speculated on Twitter that Fontes and other Democrats could be “in the back room with ballots.” Fontes fired back that he was “having coffee with an old friend,” adding, “Stop with this conspiracy garbage.”

More broadly, the state’s top Democratic candidates urged patience, with Hobbs writing on Twitter, “Accurate election results take time.” Kelly thanked his supporters on social media, writing, “I’m confident we’re going to win. But we don’t have the final results yet.”

Lake was holed up Wednesday in meetings with advisers, outside allies and people who may ultimately serve in her administration. Among them was Floyd Brown, a longtime conservative operative and founder of the news and opinion website the Western Journal, according to two people familiar with the discussions, one of whom said it was an advisory meeting. They spoke on the condition of anonymity to talk about private discussions. Brown, who did not respond to a request for comment, suggested on social media that the mechanical issues in Maricopa County were an “effort to stop” Lake.

Lake also met with Eileen Klein, the former chief of staff for former Arizona governor Jan Brewer, a Republican; Danny Seiden, who heads the Arizona Chamber of Commerce and previously worked for Gov. Doug Ducey (R); and Tyler Bowyer, chief operating officer of the political arm of Kirk’s Turning Point USA. None commented on the meetings.

Maricopa officials said that while they did not yet know the underlying cause of the faint printing on some ballots, the problem appeared to be fixed by late Tuesday afternoon when technicians changed a setting to allow for a heavier kind of paper.

Printers like those used by the county contain “fusers” — heated rollers that melt toner and make it stick to paper. Different weights of paper require different temperatures for the toner to adhere properly.

The county has about 760 printers for printing ballots on demand, according to Megan Gilbertson, communications director for the county’s elections department. About 600 of those were made by Oki, a corporation headquartered in Japan, which discontinued all sales of its printers in the United States in March 2021. Oki has said it continues to supply parts, software updates and other services. Gilbertson said those printers are the ones that had problems.

“It is standard practice to continue to use equipment if an organization can continue to maintain it,” Gilbertson said. Dennie K. Kawahara, the president and chief executive of Oki Data Americas, said in an email that the firm had received no inquiries or customer service requests relating to the problem in Maricopa County. “The printers were tested prior to the election and were working fine,” Kawahara wrote.

Maricopa’s 2022 elections plan said each of the county’s 223 polling places would have two or three printers and that this would provide enough capacity in case some malfunctioned.

Gilbertson said each ballot printer was linked only to a laptop and that they were not connected to one another or to the internet. The printers’ settings could only be changed manually and changes require a password, she said.

Swaine and Davis reported from Washington. Cat Zakrzewski in Washington contributed to this report.