LUMBERTON, N.C. — The congressional campaign of Mark Harris disclosed late Thursday night that it owed more than $34,000 in connection with an absentee ballot and voter turnout operation that has prompted fears of election fraud and called the North Carolina Republican’s narrow victory into question.

Then on Friday, after days of silence, Mr. Harris said he would be open to a new election if an investigation into fraud allegations “finds proof of illegal activity on either side to such a level that it could have changed the outcome of the election.’’

Mr. Harris, whose campaign has received a subpoena, said in a recorded statement posted on Twitter that he was “cooperating fully” with the investigation and that he “absolutely unaware of any wrongdoing.”

“I trust that this investigation will be full and complete, examining any alleged irregularities that could have benefited either party in this election or past election cycles,” he said. “I’m hopeful that this process will ultimately result in the certification of my election to Congress before the next House session begins.”