Judge Margaret R. Mahoney said it was too soon to require Maricopa and other counties to stop contacting voters to verify signatures on mail ballots. She also declined to order the counties to temporarily separate mail ballots that have been verified by that process after Election Day.
County registrars said that would cause chaos and slow the long vote-counting process even more.
Mahoney scheduled a hearing Friday and indicated she would rule then.
The lawsuit came hours before Democrat Kyrsten Sinema jumped into a slight lead over Republican Martha McSally in the midst of the slow vote count. Sinema is ahead by about 9,000 votes out of 1.9 million counted so far. About 400,000 remain to be counted in the race to replace retiring Republican Sen. Jeff Flake.
The suit alleges that the state's county recorders don't follow a uniform standard for allowing voters to address problems with their mail-in ballots, and that Maricopa and Pima counties improperly allow the fixes for up to five days after Election Day. Sinema has gained votes recently from Maricopa, and Pima is a Democratic bastion.
Lawyers who filed the suit say they'd be happy if Mahoney decided to order the state's more rural counties to follow the same procedures, which would have the effect of expanding the vote count.
Currently, several other counties that lean Republican destroy mail ballots if voters don't help verify their signatures before polls close on Election Day.
"At the end of the day, each vote should be treated the same way," attorney Bret Johnson said in an interview.
Recorder Adrian Fontes, the official in charge of counting ballots in Maricopa County, home to 60 percent of Arizona voters, said his office would not finish tallying votes for another week.
"We know there's urgency out there, but we want to get it right, not quick," he said.
Arizona is notoriously slow at tallying ballots even though about 75 percent of votes are cast by mail. Those ballots must go through a laborious verification process.
If the signature on the envelope does not match the signature on the voter file, elections officials can contact the voter to try to resolve the discrepancy. Such situations arise, for example, when voters have Parkinson's disease and can no longer sign as they did in the past.
At Thursday's hearing, officials from the state's 15 counties suggested the lawsuit only involves a fraction of votes. Colleen Connor, deputy Maricopa County attorney, said there were only 5,600 votes in Maricopa that would fall under the lawsuit and that the rates elsewhere also appeared low.
Fontes said part of the logjam is due to his office's computer system dating from the 1980s, when Maricopa was far smaller and only a handful of its residents voted by mail.
He said the system only allows his office to tally about 75,000 votes a day.
The two Senate campaigns have long braced for a slow vote count. McSally is no stranger to the issue. It took The Associated Press 12 days to declare a winner in McSally's first race for Congress, which she narrowly lost.
On Thursday, she tweeted: "Woke up this morning dreading a long and painful process. I've been here before, and now, here I am again.the dentist's chair." She attached a photo of herself leaning back at the dentist's office, about to get her teeth examined.
For AP's complete coverage of the U.S. midterm elections: http://apne.ws/APPolitics
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