The state's Senate will need to approve the bill one more time before it can go on to the House. Monday's tally was 37-3; a final vote will be held Tuesday.
North Carolina has seen two attacks in as many days on the barrier islands just off its coast. In separate incidents last week, two people were attacked in South Carolina.
Police are still searching for a suspect in the attack, described as a young white man. Charleston police chief Gregory Mullen says the shooting will be investigated as a hate crime.
The Rev. Clementa Pinckney, who was also a state senator, was among nine people killed in a shooting Wednesday. In 2001, he said he was called to preach at age 13 and wanted "to make a difference."
African Americans are going to be key to a Hillary Clinton presidential run. After a tense 2008 primary fight with Barack Obama, she's trying to win them over.