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(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.”