SAN FRANCISCO — A federal judge in Los Angeles on Friday refused to block the Sept. 14 recall election, which opponents had challenged on the grounds it violated constitutional guarantees of one person, one vote.

U.S. District Judge Michael W. Fitzgerald, an Obama appointee, said there was “nothing unconstitutional about placing in one ballot a vote for or against the recall of the governor and then a vote for a replacement candidate.”

The lawsuit, filed by civil rights lawyer Stephen Yagman on behalf of a recall opponent, sought a court order blocking the election or requiring the ballot of replacement candidates to include Gov. Gavin Newsom. Under California’s recall rules, Newsom is not permitted to run as a replacement candidate, and he could be replaced by a candidate who received far fewer votes.

“No doubt, it would be cheaper and simpler to replace a sitting governor with the lieutenant governor,” Fitzgerald wrote. “But for over one hundred years, California has chosen a different procedure. The United States Constitution does not prevent that.”

Fitzgerald also said the late filing of the lawsuit — Aug. 13 — means it “seeks to halt an election that, in fact, has already begun.”

The voter who brought the suit was “disgruntled that a replacement candidate with a small plurality might replace a sitting governor who, based on a robust ‘No’ vote, might well have beaten that same replacement candidate in a general election,” the judge wrote.

“As that may be,” he added, “such disgruntlement raises no federal constitutional issues and certainly does not give the federal judiciary the right to halt the mammoth undertaking of this gubernatorial recall election.”