WASHINGTON — On election night, in the back room of an exclusive country club outside of Charlotte, N.C., Mark Harris, a pastor turned politician, gathered a small group of friends and advisers to pray as they waited for the results.

A longtime friend and fellow pastor, Mike Whitson, assured Mr. Harris, the Republican congressional candidate for North Carolina’s Ninth District, that “it was God who sets up kings” and that “God could be trusted with the outcome” of this race. Mr. Harris won by just 905 votes, and jubilation set in.

But now, a month later, the story of Mr. Harris’s path to victory appears far from a divine anointing.

In one of the most dramatic developments of the November elections, state-election officials have refused to certify Mr. Harris’s victory over Dan McCready, a Democrat, and are investigating potential voter fraud after questions emerged over irregular absentee ballot activity, allegedly involving a consultant hired to advance Mr. Harris’s campaign efforts. Congressional Democrats are calling for an emergency hearing. On Thursday, the executive director of the North Carolina Republican Party said he would be open to holding a new election, and on Friday Mr. Harris said he would be as well if fraud occurred that changed the election’s outcome.