Kris W. Kobach, the secretary of state of Kansas and face of the Trump administration’s efforts to clamp down on supposed voter fraud, was found by a federal judge on Wednesday to have disobeyed orders to notify thousands of Kansans in 2016 that they were registered to vote.

Mr. Kobach, who served last year as the vice chairman of the Trump administration’s short-lived presidential commission on voter fraud, was reprimanded in a 25-page ruling by Federal District Judge Julie A. Robinson of Kansas, who held him in contempt of court.

Mr. Kobach has championed restrictive laws on voting around the country, warning that voting fraud is rampant and unchecked, despite widespread agreement from election experts that it is extremely rare. But voting rights advocates pointed to the judge’s findings as a counter to Mr. Kobach’s efforts to position himself as a protector of the voting process.

“Secretary Kobach likes to talk about the rule of law,” Dale Ho, director of the Voting Rights Project at the American Civil Liberties Union, said in a statement. “Talk is cheap, and his actions speak louder than his words.”