Murkowski, with a campaign war chest that contained upward of $1 million and high name recognition, jumped back into the race.
The state has tentatively set election certification for Nov. 29.
Assistant Attorney General Margaret Paton-Walsh said by e-mail that no hearing has been scheduled and Judge Beistline could render a decision without one.
Campbell was out of town Thursday. Division of Elections Director Gail Fenumiai, who reviewed disputed ballots and decided wither they should be credited to Murkowski, said by e-mail she had not seen the latest court filing and had no comment.