Writing in the Wall Street Journal, Mike Pence said the Religious Freedom Restoration Act (RFRA) had been "grossly misconstrued" as anti-gay.
"I abhor discrimination," he wrote, rejecting claims the law limited the rights of gays and lesbians.
The measure gives firms and groups the right to express their religious beliefs in the way they do business.
The governor went on the attack after a number of famous names, corporations and sporting institutions warned that business owners now had a licence to discriminate against gays and lesbians.
Signed into state law last week, the bill prevents the state from forcing people to provide services they say are contrary to their religion.
Critics believe it provides a way for opponents of gay marriage, which became legal in Indiana last year, to continue their opposition by other means.
The backlash has made allies of Hillary Clinton and Miley Cyrus, and Angie's List and Apple.
And the National Collegiate Athletic Association said it was "especially concerned" about how the law would affect its athletes, days before its basketball finals are being held in Indianapolis.
A day after an awkward television interview in which he refused to answer questions about how the law might be used against gay people, Mr Pence had a clearer message for readers of the Wall Street Journal.
"I abhor discrimination. I believe in the Golden Rule that you should 'do unto others as you would have them do unto you.'
"If I saw a restaurant owner refuse to serve a gay couple, I wouldn't eat there anymore.
"As governor of Indiana, if I were presented a bill that legalised discrimination against any person or group, I would veto it."
Mr Pence has found himself under intense pressure to amend the law, as other US states have done, to add anti-discrimination language.
Fellow Republicans in the state's Senate and House have offered to explore that possibility, after receiving a letter from nine chief executive officers, including the heads of Angie's List and Eli Lilly, to "take immediate action".
The White House, Walmart and the mayor of Indianapolis have also expressed concerns.
Connecticut Governor Dan Malloy signed an executive order on Monday that bans state-funded travel to Indiana and other states that simultaneously have RFRA and yet no balancing law to protect gays and lesbians from discrimination.
The governor of Indiana has defended a new law that has unleashed a wave of condemnation across the country.