ALEXANDRIA, Va. — A federal judge on Wednesday rejected an effort to block the Virginia elections board from certifying the results in a House of Delegates race where election officials say some voters got the wrong ballots.

Three voters, represented by a law firm closely aligned with the Democratic Party, asked a judge in federal court in Alexandria to block the certification in a race that could determine control of the House.

The elections board, controlled by Democrats, is scheduled to meet Monday, and officials there say they will have little choice but certify Republican Bob Thomas as the winner over Democrat Joshua Cole in the 28th District in the Fredericksburg area.

Though three races, including the Thomas-Cole race, remain too close to call and subject to possible recounts, Republicans would hold a 51-49 advantage in the chamber if their leads hold up in those three races. In one of the races, the Republican candidate leads by only 10 votes out of tens of thousands cast.

Thomas currently leads Cole by just 82 votes in the Fredericksburg-area race. Elections board lawyers said at Friday’s hearing that they have so far identified 384 voters who were assigned to the incorrect district, though they did not say how many actually turned out to vote, and they said that figure could include voters not just who were wrongly excluded from the district, but voters who were wrongly included in the district as well. It remains unclear how the problem arose.

After Wednesday’s emergency hearing, conducted by telephone conference, Judge T.S. Ellis III said it’s too early for federal intervention, and said the state process, including possible recounts and contesting the results of the election to the General Assembly, should run its course.

“Federal courts ought to interfere as little as possible in state matters of this sort,” he said.

Ellis also said that the plaintiffs could not yet show that the mistakes that occurred were any more than garden-variety errors that fail to rise to the level of a constitutional violation requiring federal intervention.

Still, he rejected arguments made by Republican lawyers that the federal courts had no role whatsoever. He said it’s conceivable that a full investigation of the errors could eventually necessitate a need to intervene and order a new election.

“This isn’t the end of the issue,” he said. “This case goes on despite denial of the temporary restraining order.”