Indiana Governor Mike Pence on Sunday defended a new state law that opponents worry may support discrimination against gay people, saying he had no plans to add extra protections but would consider new suggestions from state legislators.

Pence, speaking on ABC's "This Week," sought to counter criticism from protesters who have spilled onto the streets of Indianapolis and others, including some corporations, after signing the Religious Freedom Restoration Act on Thursday.

"There has been shameless rhetoric about my state, about this law, and about its intention all over the Internet," Pence said. "It does not apply to disputes between individuals, unless government action is involved."

Supporters say the law, which was passed overwhelmingly by the Republican-led state legislature, will keep the government from forcing business owners to act against their strongly held religious beliefs.

Opponents say it may allow vendors to discriminate against gay, lesbian, bisexual and transgender people and that its reach is also much broader than other states' religious freedom laws.

The Indiana law has drawn criticisms from companies such as Angie's List Inc and Wal-Mart Stores Inc, tech industry chiefs including openly gay Apple Inc CEO Tim Cook, and the White House.

"Discriminatory legislation is bad for Indiana and for business," said Janice Chavers, director of human resources for Indianapolis, Indiana-based Eli Lilly and Co.. The company is concerned that "divisive actions like this" divert the state's attention from education and economic development, and could make it harder to recruit and retain employees, Chavers said.

Pence said he would not pursue efforts to add sexual orientation as a protected class under the state's civil rights laws, which has been floated as a possible recourse.

"I will not push for that," he said. "That's not on my agenda and that's not been an objective of the people of the state of Indiana."

Similarly, he said he would not change the law to make clear that it would not establish or eliminate a defense in claims under any laws protecting civil rights or preventing discrimination.

"But if the General Assembly in Indiana sends me a bill that adds a section that reiterates and amplifies and clarifies what the law really is ... then I'm open to that," Pence said.

Gay rights groups worry it will be used by businesses that do not want to provide services for same-sex weddings. Gay marriage became legal in Indiana last year, following an appeals court ruling.

Pence did not directly answer whether the law would protect a Christian florist who may deny service to a gay couple, as he argued that the legislation was not about discrimination:

"The issue here is, you know, is tolerance a two-way street or not?"

The National Collegiate Athletic Association (NCAA), which is holding its premier men's' college basketball championship in Indianapolis next weekend, said the organization was concerned about the legislation's impact on its employees and student-athletes.

"Moving forward, we intend to closely examine the implications of this bill and how it might affect future events as well as our workforce," NCAA President Mark Emmertsaid in a statement.

The LGBT Sports Coalition has called for organizations to pull all major sporting events from Indiana. The group wants the 2016 Women's Final Four and all future NCAA basketball tournament games pulled from Indiana as well as other sporting events.

"We believe any sporting events that can be moved outside the state should be moved," the coalition said in a statement.