The party's executive committee decided Thursday there was not enough evidence of impropriety to nullify the June 8 election victory by Alvin Greene. The 32-year-old lives with his father and waged no visible campaign.
The decision nixed a bid for another primary by candidate Vic Rawl, who contended he lost because of problems with electronic voting machines.
Party officials pushing against a new election say they need to move past the primary and focus on other races.
Greene will face Republican Sen. Jim DeMint, who is considered a heavy favorite.
