When the Department of Homeland Security sent Nevada a list of 185 names last month that it claimed identified noncitizens who had been improperly allowed to register to vote, state election officials got to work. On Tuesday, the state sent a strongly worded rebuke to the federal government: Every single person on the list was a lawful citizen.

"As for the 185 individuals, our records indicate that they were citizens," Greg D. Ott, a deputy attorney general in Nevada, wrote. "You have provided nothing of substance to suggest otherwise." Mr. Ott also stated that D.H.S. officials had still not provided enough data for election officials to investigate their claims.

"Our records do not support DHS's claims, and DHS has still not provided evidence to change that," Francisco Aguilar, the Democratic secretary of state in Nevada, said in a statement. The back and forth began in July, when President Trump and Markwayne Mullin, the homeland security secretary, said they had identified more than 270,000 noncitizens on voter rolls in just four states: Nevada, California, New Jersey and Pennsylvania.

In Nevada's case, Mr. Mullin initially claimed that there were as many as 15,903 noncitizens on the voter rolls. But in a meeting between Nevada election officials and the Department of Homeland Security last month, department leaders admitted that their initial claim was unsubstantiated. Now, Nevada officials are saying even that 185 number is wrong.