Carilek said she was calling in lawyers and gathering evidence from voters who had trouble voting because she refused to recognize the Arizona governor’s race.
The Republican candidate said she was considering her next move after her Democratic opponent, Katie Hobbs, announced her candidacy.
In a two-and-a-half-minute video, Ms. Lake did not offer to throw in the towel.
Before the election, she declined to say whether she would throw in the towel if she lost.
Ms Lake said: “Rest assured, I have assembled the best and brightest legal team and we are exploring avenues to right the many wrongs that have occurred over the past week.
“I’m doing everything in my power to right those wrongs.”
The staunch Trump supporter pointed to problems with ballot printers at about a third of polling centers in Maricopa County, Arizona’s largest county, and long lines at some polling places.
She claimed the issues disenfranchised voters who couldn’t wait at the polls, adding: “What happened to Arizonans on Election Day is inexcusable.”
County election officials said all ballots had been counted and voters could go to any polling place in the county, many of which had little or no lines and wait times were posted online.
Election officials traced the problem to a printer setting that sometimes caused ballots to be printed too lightly for tabulators in the field to read.
They said they used the same setup in the August primaries and preelection tests without widespread problems.
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Some 17,000 ballots were not scanned at the precinct-based counts, but were placed in a collection box to be counted by more advanced machines at the county’s elections headquarters, which came to be known as “Box Three.”
Bill Gates, the Republican chairman of the Maricopa County Board of Supervisors, blamed state Republican Chairman Kelly Ward and other high-profile Republicans for delays and long lines after they told their supporters not to use the third box.
“This team, we have accepted our responsibility in this regard,” Mr Gates said on Monday.
“But I don’t want to take responsibility for problems caused by others. I’m well aware that the queues are longer because one party leader is spreading misinformation.”
Because of the problems, Republicans asked judges to extend polling hours, but the judges declined, saying they had not presented evidence that anyone had been disenfranchised.
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Democrats overwhelmingly vote by mail, and Election Day in-person voting has a lot of support for Republicans because Ms. Lake and others in the party claim it is safer.
Ms. Lake has said little since many news organizations announced their run for Hobbs on Monday. Later on Wednesday, she released a video that included a clip of the campaign from Tom Petty’s song “I Won’t Back Down.”
The video she released on Thursday said Ms. Hobbs, the current secretary of state, should have recused herself from any office in the election.
The secretary of state develops election procedures and certifies equipment, but her office does not count ballots.