A federal judge ruled on Sunday that Iowa may continue challenging hundreds of potential ballots cast in the election on the basis that the voters might be noncitizens, a move that critics say could disenfranchise legitimate voters.

Iowa’s secretary of state, Paul Pate, a Republican, issued a letter to county commissioners last month challenging the status of 2,176 people on voter rolls, saying that they had previously identified themselves to a state agency as noncitizens. The plaintiffs in the case were four recently naturalized U.S. citizens whose voting status was challenged, despite being eligible to vote. They had asked the court for a temporary restraining order and a preliminary injunction to rescind the letter and restore the status of any voters removed from the rolls.

But Judge Stephen H. Locher of the Southern District of Iowa, who was appointed by President Biden, said that a small minority of the 2,176 registered voters — about 12 percent, or about 250 people — “are indeed registered voters who are not United States citizens,” and that granting an injunction “effectively forces local election officials to allow ineligible voters to vote.”

It is a felony for a noncitizen to vote in a federal election, potentially resulting in jail time, a fine and deportation.

Judge Locher also pointed to a U.S. Supreme Court ruling last week that allowed Virginia to purge about 1,600 people from its voter rolls in supporting his decision to allow the challenge to go forward.

But he also expressed concern at some of the directives in Mr. Pate’s letter, which he said directed local election officials to challenge the legitimacy of a voter on the list “even when the local officials themselves do not suspect the person is ineligible to vote” and “require voters on the list to file provisional ballots even when they have proven citizenship at the polling place.”

In a statement, Mr. Pate said that the ruling was “a win for Iowa’s election integrity,” adding that his role “requires balance — ensuring that on one hand, every eligible voter is able to cast their ballot while ensuring that only eligible voters participate in Iowa elections.”