(CNN) Gov. Mike Pence pledged Tuesday to "fix" Indiana's controversial religious freedom law to clarify that it does not allow discrimination against gays and lesbians.

But he insisted the problem isn't the law itself but how it's being perceived, saying a fix is needed only because of "frankly, the smear that's been leveled against this law."

And he said the fix won't involve statewide anti-discrimination protections for LGBT Hoosiers.

The first-term Republican governor sought to tamp down the backlash Indiana has faced since he signed the law -- which its in-state supporters had claimed would allow businesses to turn away LGBT customers -- last week. He said he's asking state lawmakers to send him a followup measure before this week's end to ensure that's not the case.

"It would be helpful to move legislation this week that makes it clear that this law does not give businesses a right to deny services to anyone," Pence said in a press conference in Indianapolis on Tuesday.

Pence's comments come amid intense criticism from major corporations like Apple, Walmart and tech giant Salesforce against Indiana's law and similar measures advancing in at least a dozen other states this year. The NCAA, which is set to host its men's basketball Final Four in Indianapolis, has said it could move events elsewhere in the future.

Billionaire investor Warren Buffett told CNN's Poppy Harlow on Tuesday that he's not read the law, but opposes discrimination.

"I have not read the law, and I've heard of some discussion on television. To the extent that it could in any way be prejudicial to gays or lesbians, I'd be opposed to that," he said.

He added that he has no plans on moving any of his Indiana-based business assets.

"I doubt if we'd move them. The individual managers of our businesses make all the decisions," Buffett said.

White House Press Secretary Josh Earnest blasted Pence on Tuesday, saying the governor has tried to "falsely suggest" that Indiana's law simply mirrors a federal religious freedom law signed by President Bill Clinton.

That, he said, is "not true" because the Indiana law "a much more open-ended piece of legislation that could reasonably be used to try to justify discriminating against somebody because of who they love."

"We see business leaders saying that they are reluctant to do business in a state where their customers or even their employees could be subjected to greater discrimination just because of who they love," Earnest said.

"That's not fair. It's not consistent with our values as a country that we hold dear," he said. "And I think that's what has provoked the strong outcry, and I think it's what has provoked the previously defiant governor to consider a position of changing the law."

Republican contenders for the party's 2016 presidential nomination, meanwhile, have rallied to Pence's defense. Jeb Bush, Marco Rubio, Ted Cruz and several other likely candidates said Monday evening that they support religious freedom laws.

Democrats, meanwhile, have criticized Indiana's law. Hillary Clinton tweeted that it's "sad this new Indiana law can happen in America today." Former Maryland Gov. Martin O'Malley called it "shameful" during an appearance in New Hampshire on Tuesday.

The debate touched a raw nerve in Indiana, which is just a year away from an emotional battle over a Republican-driven proposal to amend the state's constitution to ban same-sex marriage.

Just months before the Supreme Court is set to rule on whether same-sex marriage is legal everywhere in the United States, the religious freedom debate has offered a look at the next front in America's culture clashes -- and the cross-currents facing the Republican Party, with social conservatives seeing religious freedom laws as sturdier ground and the typically pro-GOP business community and younger voters seeing those measures as veiled efforts at discrimination.

"Was I expecting this kind of backlash? Heavens no," Pence admitted Tuesday.

He'd waffled in recent days over whether or not he would support a legislative fix to the law before finally announcing that he wanted one -- but he didn't say what that fix would be.

Potentially complicating his effort to quell the criticism, Pence said he opposes adding sexual orientation to the list of Indiana's protected categories under state anti-discrimination law.

Democrats who'd seen their proposals to do just that rejected by the legislature in recent months said only a solution along those lines would suffice.

"You have to take affirmative action -- you can't just tinker with this language," state Senate Democratic leader Tim Lanane said.

Pence's statement came a day after Indiana's top state legislators announced they were working on a legislative fix to clarify the intent of the law and following an intense backlash against the law, especially from the business community in Indiana and across the country.

Pence and other Indiana Republicans have repeatedly insisted that the law was never intended to allow discrimination against anyone and have charged that, even in its current form, the law could not be used as a legal defense to discriminate against someone on the basis of sexual orientation.

Instead, Pence and his GOP allies have accused the media and opponents of the law of mischaracterizing the law and spreading misinformation. But opposition to the law was swift and broad-sweeping, with large organizations and top companies ranging from the NCAA to Apple and Salesforce raising red flags over the law.

The state's House speaker, Brian Bosma, said he "didn't see that [reaction] coming" in the Monday press conference announcing work on a legislative fix.

Pence, the Indiana Republican who has been floated as a potential 2016 presidential candidate, again repeated that he is unflinchingly opposed to discrimination.

He also noted that he joined civil rights icon Rep. John Lewis in a march across the Edmund Pettus Bridge to commemorate the anniversary of Bloody Sunday, when hundreds of activists fighting for civil rights for African-Americans were brutally assaulted by police officers.

Pence did get some beefy backup from the field of potential 2016 presidential contenders as former Gov. Jeb Bush, Sen. Marco Rubio, Gov. Bobby Jindal and others, including the only declared 2016 presidential candidate Sen. Ted Cruz, rushing to defend the Indiana law.