DesJarlais, a physician, was set back by 2012 revelations that he had extramarital affairs with patients and encouraged his then-wife to get abortions, despite campaigning as an antiabortion conservative.
Tracy's campaign said in a statement that "there are ballots left be counted," an apparent reference to outstanding provisional and absentee ballots.
According to the Nashville Tennessean, Tracy declared victory at one point Thursday evening.
State law on recounts is vague. It allows for a court or election officials to order a recount in the case of a tie, indications of fraud or malfunction, or for other reasons that would make one necessary.
The winner will face Democratic nominee Lenda Sherrell in November and will be heavily favored to win, given the district's heavy rightward tilt.