Although studies repeatedly show voter fraud of the type Mr. Kobach targets to be extremely rare, he has not toned down his message. “We have had many, many cases of noncitizens registered to vote prior to our new law,” he said.

When pressed in a hearing in the State Legislature in January, however, Mr. Kobach said his office identified only 20 noncitizens who had registered before the new law, and just five who had actually voted.

Another of Mr. Kobach’s programs, Interstate Crosscheck, which compares voter registrations from about two dozen states to seek evidence of double voting, has also come up short in identifying significant fraud: He acknowledged only 12 cases of people voting in Kansas and another state in 2012. Six have been referred to prosecutors, he said, but so far no charges have been brought.

Democrats argue that many restrictions enacted to fight allegations of fraud end up suppressing voter turnout. Last week, the Government Accountability Office, a nonpartisan congressional research arm, reported that turnout in Kansas had declined 1.9 percent because of its ID law, especially among blacks and young voters.

Mr. Kobach criticized the report’s methodology. “We think of the G.A.O. as nonpartisan, but nonpartisan does not mean competent,” he said in an interview in his office, where laminated articles about him in Time magazine and other national publications hang on the wall.

Ms. Schodorf, a former Republican state senator who switched parties after a purge of legislative moderates by Governor Brownback, accused Mr. Kobach of creating a “mess” in the secretary of state’s office while traveling the country to pick ideological fights. These include lobbying the Texas Legislature to allow shooting feral hogs from helicopters.