On Thursday, Pence signed the controversial bill granting strongly religious people the right to refuse services for same-sex couples.
"I support religious liberty, and I support this law. But we are in discussions with legislative leaders this weekend to see if there's a way to clarify the intent of the law," Pence was quoted as saying by the newspaper Sunday.
The governor is said to have acknowledged, however, that Indiana's image had been dealt damage by the controversy surrounding the new law.
The RFRA was passed by Congress and signed into law by President Bill Clinton in 1993. In 1997, US Supreme Court ruled that the federal law does not apply to states.
The bill was approved in Indiana on Monday by 63 votes against 31. Five Republicans and 26 Democrats opposed the bill, according to the newspaper.
