The release mentions three Election Integrity experts as saying that "with a reasonable degree of statistical and mathematical certainty...election fraud occurred". Despite losing the election by 21,924 votes, Moore argued in a lawsuit filed Wednesday night that there was "election fraud sufficient to overturn the outcome of the election".
However, Merrill told The Associated Press that he isn't planning to delay the canvassing board meeting and said he has not yet found any evidence of election fraud.
Moore had filed a lawsuit late Wednesday night in an 11th-hour attempt to stop Alabama from certifying Jones as the victor.
Speaking with CNN's Dana Bash on Thursday, Moore campaign spokeswoman Janet Porter issued the warning to Gov. Kay Ivey (R) and Secretary of State John Merrill, who are set to meet this afternoon to certify Jones.
Just days after the election, the Moore campaign emailed supporters asking for donations that would be used for an "election integrity fund" to investigate and submit cases of voter fraud and other irregularities. A state judge denied Moore's request to stop the process.
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While ultimately unsuccessful, Moore's efforts to cast doubt over the election process took a page out of President Donald Trump's playbook.
After his appointment as U.S. attorney in Birmingham in 1997, Jones led a team of federal and state attorneys during trials that resulted in the convictions of Thomas Blanton Jr in 2001 and Bobby Frank Cherry in 2002.
In the complaint, Moore's attorneys noted the higher than expected turnout in the race, particularly in Jefferson County, and said Moore's numbers were suspiciously low in about 20 Jefferson County precincts.
Jones got his start in government as an aide to the last Democrat to serve a full term in the Senate from Alabama, the late Howell Heflin.
Moore's complaint also names Jefferson County Probate Judge Alan King as a defendant, alleging an "implausible" difference between his vote totals and general Republican ballot results in Jefferson County.
Prominent conservatives who allege voter fraud is more prevalent than evidence now suggests declined to add their voice to Moore's complaint.