The U.S. Supreme Court turned down a request on Monday to hear an appeal from a former New Mexico county commissioner who was removed from office after taking part in the Jan. 6 riots at the Capitol.

Couy Griffin, formerly a commissioner in New Mexico’s Otero County and the founder of “Cowboys for Trump,” was convicted in 2022 of trespassing at the Capitol. That same year, Mr. Griffin became the first public official in more than a century to be disqualified because of a constitutional ban on insurrectionists holding office contained in a provision of the 14th Amendment.

As is its custom, the court gave no reasons for turning away the appeal. The order on Monday means that Mr. Griffin will remain barred from running or holding public office in New Mexico.

The Supreme Court declined to hear Mr. Griffin’s appeal two weeks after it said Colorado could not use that same provision to stop former President Donald J. Trump from appearing on the state’s presidential primary ballot. The Colorado Supreme Court — taking on a case that was brought by six Colorado voters — had ruled in December that Mr. Trump had engaged in insurrection and was barred from holding public office.

In overturning that decision, the nine justices unanimously sided with Mr. Trump, saying states could not bar presidential candidates from ballots, though there was disagreement among the justices as to the scope of what the ruling should have addressed. The majority said that Congress was responsible for enforcing the provision against federal officeholders and candidates.

In simply letting the New Mexico ban stand, the court left some questions unresolved.

Mr. Griffin’s lawyer, Peter Ticktin, said he believed the court’s order means his client remains banned for life from state and federal office. “This puts Couy in a class of his own,” Mr. Ticktin said. “He is the only American to have been removed from office based on the 14th Amendment, and we are looking to see if there is a way to return to the courts of New Mexico so that justice can be done.”

He added: “We all know that the proceeding against Couy was contrary to law now that the Supreme Court decided the Trump case and defeated the attempt to have him taken off of the Colorado ballot.”

Noah Bookbinder, president of Citizens for Responsibility and Ethics in Washington, which brought the case against Mr. Griffin, said that the court “kept in place” the finding that Jan. 6 was an insurrection. “Now it is up to the states to fulfill their duty under Section 3 to remove from office anyone who broke their oath by participating in the Jan. 6 insurrection,” he said.

In a post on social media after the order, Mr. Griffin had his own interpretation: “I’m officially barred thru a court order of running for any other office other than the office of President. I wonder if that holds true to the office of Vice President?”

In a later post, he said that he had filed an appeal on the charge of trespassing.

“It only takes one card to bring the house down! Still praying for justice. Trump Card!!” Mr. Griffin wrote.

On Jan. 6, 2021, Mr. Griffin, an avowed denier of the 2020 election results, burst through barricades at the Capitol, accompanied by a videographer, and addressed the crowd with a bullhorn. He did not enter the building.

For months before the Jan. 6 riots, Mr. Griffin had attended Stop the Steal rallies and attempted to recruit protesters to head to Washington, Judge Francis J. Mathew of the New Mexico District Court wrote in his decision barring Mr. Griffin from future office.

In March of 2022, Judge Trevor N. McFadden, presiding in the Federal District Court in Washington, found Mr. Griffin guilty of one misdemeanor count of trespassing and acquitted him of another charge of disorderly conduct. Mr. Griffin was sentenced to 14 days in prison.

Six months later, Judge Mathew issued his ruling — in response to a suit filed by Citizens for Responsibility and Ethics in Washington — that Mr. Griffin was to be removed from office under Section 3 of the 14th Amendment, which was adopted during the Reconstruction era in an attempt to block members of the Confederacy from holding office.