In declaring him the winner, Raleigh's WRAL-TV reported unofficial results gave Burr 80 percent of the vote on the GOP side.
With 83 percent of the precincts counted, the TV station said it appeared Democrats Elaine Marshall, North Carolina's secretary of state with 37 percent, and Cal Cunningham, a former state senator with 27 percent, were headed to a runoff.
North Carolina Democrats think they can knock off Burr, plagued by poor poll numbers, in November.
WRAL said incumbent U.S. Reps. G.K. Butterfield, Walter Jones and Howard Coble notched easy primary victories. The station said Renee Ellmers won the Republican primary in the 2nd Congressional District and will go against incumbent Democrat Bob Etheridge in the fall general election.