By Steve Barnes

LITTLE ROCK, Ark. (Reuters) - Republican Arkansas Governor Asa Hutchinson on Wednesday rejected a religion bill he had said he would sign into law, reversing course after a national firestorm of criticism assailing such legislation as discriminating against gays and lesbians.

In a news conference Hutchinson said he was sending the Religious Freedom Restoration Act (RFRA) back to the Republican-controlled state legislature for a rewrite to better balance tolerance for diversity and protections of religious freedom.

The governor said his own son had asked him to veto it, adding a personal element to the intense pressure to reject the bill he had already faced from businesses such as Arkansas-based Wal-Mart Stores Inc, the world's biggest retailer.

"We want to be known as a state that does not discriminate, but understands tolerance. That is the challenge that we face," Hutchinson said. "We just didn't get it perfect through that legislative process."

Hutchinson's reversal came a day after Indiana Governor Mike Pence, also a Republican, said he was sending his state's RFRA back for a rewrite for the same reason.

Pence suffered national outrage after he signed Indiana's bill into law last week. On Wednesday Republican lawmakers in his state met with leaders of the lesbian, gay, bisexual and transgender community to see how they could modify the law to protect their community from potential discrimination.

Twenty U.S. states and the federal government have RFRA, which allow individuals to sue the government if they believe their First Amendment religious rights have been violated.

But Indiana and Arkansas's go further than all but one of the other state laws, allowing lawsuits between private parties. That raised the possibility that businesses such as photographers or florists could use the law as a defense if they are sued for refusing to provide services for same-sex weddings. Texas is the only other state with a similar provision.

Hutchison said he was asking lawmakers to bring the Arkansas RFRA in line with the federal one, which does not include the language on lawsuits between private parties.

Critics see the crafting of the newest RFRAs in Arkansas and Indiana as a push-back against the expansion of gay-marriage acts to most states last year.

(Reporting by Fiona Ortiz in Chicago, Jon Herskovitz in Austin, Texas, David Bailey in Minneapolis, Suzannah Gonzales in Chicago and Lawrence Hurley in Washington, D.C.; Editing by James Dalgleish)