Moore has refused to concede the election, which he had been widely expected to win before allegations of sexual misconduct with underage girls emerged late in the campaign. Moore has denied all of the allegations.
The Alabama State Canvassing Board is scheduled to meet Thursday afternoon to certify Jones' victory. But the Moore campaign filed a complaint late Wednesday night in state circuit court in Montgomery, the state capital, seeking a temporary restraining order to postpone the certification, alleging "potential election fraud that improperly altered the outcome of this election."
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"This is not a Republican or Democrat issue as election integrity should matter to everyone," Moore said in a statement released by the campaign.
Alabama Secretary of State John Merrill told The Associated Press on Wednesday evening that he has no intention of delaying the canvassing board meeting.
“It is not going to delay certification and Doug Jones will be certified (Thursday) at 1 p.m. and he will be sworn in by Vice President Pence on the third of January,” Merrill said.
Moore's statement gives few details of the purported irregularities, which it says were substantiated "with a reasonable degree of statistical and mathematical certainty" by three election experts.
State officials said last week that they had found no evidence of voter fraud in the Alabama Senate race.
In his election complaint, Moore said that he took a polygraph test days after the Dec. 12 election in regard to sexual misconduct allegations made by three women — Leigh Corfman, Beverly Nelson and Tina Johnson.
"As I had expected, the results of the examination reflected that I did not know, nor had I ever had any sexual contact with, any of these individuals," Moore claimed in an affidavit included in the complaint, adding that the allegations are "false and malicious attacks."
Alex Johnson is a reporter and editor for NBC News based in Los Angeles.