A county judge in Georgia has rejected an argument by allies of former President Donald J. Trump that local election officials have the power to refuse to certify election results, finding the process to be mandatory and one that must meet critical deadlines.

The ruling cuts at the heart of a key argument from right-wing activists following the 2020 election, when Mr. Trump sought to disrupt the certification process as part of his bid to subvert the results. In years since, right-wing groups have been seeking much broader authority and power over the certification process, an ambitious — and legally dubious — attempt to reimagine decades of settled law.

In May, Julie Adams, a member of the Fulton County Board of Elections and a close ally of right-wing election activists in Georgia, filed a lawsuit arguing that she had the right to refuse to certify an election.

But Judge Robert C.I. McBurney ruled on Monday evening that the effort to wrest control of certification was unconstitutional and against state law, and that law enforcement and the courts remained the proper venue for any investigations, challenges or concerns about the integrity of an election.

“If election superintendents were, as Plaintiff urges, free to play investigator, prosecutor, jury, and judge and so — because of a unilateral determination of error or fraud — refuse to certify election results, Georgia voters would be silenced,” Judge McBurney wrote. “Our Constitution and our Election Code do not allow for that to happen.”

Lawyers for Ms. Adams did not immediately respond to requests for comment on Tuesday.

Judge McBurney acknowledged in his ruling that debates over certification had confused some local election officials, and he sought to clarify their role.

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