Indiana Governor Mike Pence, facing a firestorm of criticism, said Tuesday he and state legislators will work to "fix" a contentious new law this week that some warn discriminates against gays.

Addressing a packed press conference, Pence insisted the law signed last week "does not give anyone a license to discriminate."

But amid threats of crippling boycotts, the state's largest newspaper demanded that Pence "fix this now" by taking immediate action to avoid further damaging to Indiana's reputation.

"We've got a perception problem," the embattled Republican governor acknowledged, but he stopped short of saying the law will be repealed.

"After much reflection, and in consultation with leadership of the general assembly, I've come to the conclusion that it would be helpful to move legislation this week to make it clear that this law does not give businesses a right to deny services to anyone," Pence said.

"It's a fix of a bill that through mischaracterization and confusion has come to be greatly misunderstood. And I'm determined to address this this week and to move forward as a state."

Indiana, where same-sex marriage has been legally recognized since last October, has faced a tsunami of criticism since the legislature passed the Religious Freedom Restoration Act.

Supporters insist the law protects people or businesses from infringement on their religious beliefs.

But critics including gay rights activists say it lets Indiana businesses whose owners reject homosexuality on religious grounds turn away LGBT customers.

The law specifically allows individuals and businesses who face discrimination lawsuits to use the defense that serving homosexuals "substantially burdened" their religious freedom.

- Rebukes from national businesses -

The issue has sparked a national debate, with several Indiana-based organizations or events caught in the crossfire.

Critics have called on the National Collegiate Athletics Association, headquartered in Indiana, to move next weekend's Final Four basketball semifinals out of host city Indianapolis.

Companies like Apple and Yelp issued strong rebukes, and some states like Connecticut banned their government employees from traveling to Indiana.

"It's time for the people of Indiana to admit this is an unbelievable embarrassment to their state," Connecticut Governor Daniel Malloy told CNN.

Rock band Wilco announced Monday it cancelled its May 7 show in Indianapolis in response to the law, which it said "feels like thinly disguised legal discrimination."

And Jim Irsay, owner of the Indianapolis Colts, stressed that his NFL football team has "always embraced inclusiveness, tolerance and a diverse fan base."

Two Republican presidential hopefuls, Senators Ted Cruz and Marco Rubio, have come out in support of the religious freedom law.

Indianapolis Mayor Greg Ballard is Republican like Pence, but stood in staunch opposition to the law and said it was critical to tamp down the uproar now.

"We spent 30, 40 years building up this reputation as a great convention city, as a great sports event city," he told National Public Radio.

"We just can't have that hurt as much as it has been hurting."