“This disproportionately hits 18- to 24-year-olds,” said Jamie Shew, a Democrat and the county clerk for Douglas County. “For a lot of them, they say, ‘I’m not going to worry about it.’ They’re busy, and this is just one more thing to do.”

Under the law, passed in 2011, registrants must prove citizenship by producing a document from an approved list, which includes birth certificates, passports and naturalization records. They may bring the document to a county clerk’s office or email a photograph of it. Under Mr. Kobach’s new rule, if they fail to do so, they would be removed from the voters list after 90 days. Residents can try to register again even after being removed from the list.

The 36,000 people on the list represent about 2 percent of the state’s 1.7 million registered voters. The Wichita Eagle reported in September that more than 16 percent of people who have tried to register to vote since the law went into effect in January 2013 have been placed on the list.

Several people on the list who were contacted by The Times said that they did not remember trying to register to vote and had no idea why their names were on the list. Two people said that they had moved out of state since they began the registration process so had not bothered to complete it. Several others said they had wanted to vote but felt hamstrung by the requirement to provide proof of citizenship, and eventually gave up.

One of the plaintiffs in the lawsuit, Cody Keener, 21, said that he tried to register to vote while renewing his driver’s license last year and assumed that his registration was complete. Mr. Keener, a full-time student at Baker University who lives in Lawrence, Kan., said he later received a notice from the Douglas County clerk’s office that he had been marked as “in suspense” because he had not submitted proof of citizenship. Angered by that requirement, he decided to join the suit.

“I walked out of the D.M.V. under the impression that I was registered,” he said. “When I found out later that 36,000 other people were on the list, I thought about how many people would be in my shoes, and how many tens of thousands of people would show up on Election Day thinking they were registered to vote.”

Mr. Shew, the clerk for Douglas County, whose most populous city is Lawrence, which is home to the University of Kansas, said many people had expressed frustration with the law. “The part that’s disheartening to me is, you hear a lot of people on the phone say, ‘This is just too much to deal with, forget about it.’ ”