North Carolina Republican Party leaders said on Thursday they would be open to holding a new congressional election in a district roiled by fraud allegations if a state investigation finds enough evidence that the outcome of the race was affected.

Almost a month after Republican Mark Harris declared victory in his race for a seat in the U.S. House of Representatives, the North Carolina board of elections is declining to certify the result as it investigates mail-in ballots from two rural counties.

If fraud is uncovered, the board could order a new vote. Democrats in the U.S. House are also calling for an investigation and could rule on the contest when they take control of the chamber next year.