Burns ended his rematch race with Barrow, and one of the nation's closest House races, with a phone call to congratulate the Democratic incumbent. Burns, a former congressman, was ousted by Barrow in 2004.
Burns' concession came a day after the Georgia secretary of state's office released its official results from the Nov. 7 election. The tally showed Barrow won a second term in eastern Georgia's 12th District by less than 1 percent of the 142,438 votes cast.
Because the margin was so close, Burns could have requested a recount under Georgia law.
"We did not feel a recount would substantially alter the results," Burns said in conference call with reporters. "We felt it was not in the best interest of the state to go through the time and expense."