The flag issue is diverting the state's attention from more urgent issues, he said.
"I believe the people of South Carolina can figure out what to do with this flag issue."
Many political consultants say the impact of the flag issue in this year's elections is being greatly exaggerated.
Pure coincidence, aides to both men say in denying that the flag issue was discussed.
Memorial Day, a special flag issue to commemorate the 125th anniversary of the holiday.
Nearly seven years later, the Confederate flag issue has moved squarely back into the sports arena.
The Republican chairman said that the flag issue was on his list of discussion topics but that he never got to it.
Lawmakers and lobbyists acknowledged that the flag issue had probably not yet been put to rest.
The flag issue introduces a new element to a race that already features rather unusual political profiles.
But it remains unclear what effect the flag issue will have on the race.