A judge has set a hearing to consider how to handle a lawsuit filed by Republican party officials seeking to prevent some mailed-in ballots from being counted in Arizona's nail-biter of a Senate race.

RELATED: What's next for Sinema/McSally race?

County officials were still counting more than 600,000 ballots when four local Republican parties filed the lawsuit Wednesday night. The suit challenges the way counties have allowed voters to fix problems involving signatures on some mailed-in early ballots.

RELATED: FULL ELECTION RESULTS

A judge in Phoenix set the hearing for late Thursday morning to set a case schedule.

The lawsuit singles out the state's two biggest urban counties, which are the base of Democratic Rep. Kyrsten Sinema's support. She and Republican Rep. Martha McSally are separated by only a few thousand votes.

Counting outstanding votes could take a week or more.