WASHINGTON (AFP) - The US states of Arkansas and Indiana passed amended versions of religious freedom laws on Thursday following a nationwide outcry that the original legislation effectively legalized discrimination against homosexuals.

Arkansas's Republican-dominated legislature passed its "Religious Freedom Restoration Act" but without the clauses which could have allowed companies to refuse to serve gay customers on religious grounds.

Republican Governor Asa Hutchinson swiftly signed the bill into law, a day after refusing to sign the original version of the bill and urging lawmakers to think again.

The state legislature in Indiana, also Republican-controlled, meanwhile passed a new law specifically forbidding discrimination based on sexual orientation or gender, clarifying a law on religious freedom passed law week which triggered outrage.

The laws in both states were initially designed to require the state to demonstrate an important public interest before restricting the exercising of religious beliefs.

However rights groups said the laws could effectively have enabled businesses to discriminate against the lesbian, gay, bisexual and transgender community on religious grounds.

Both states received nationwide criticism over the legislation, with big businesses threatening to boycott their states. Indianapolis, which regularly hosts major conventions and sporting events, was particularly concerned that a boycott could have dealt a devastating blow to its economy.

Indiana Governor Mike Pence said Thursday the measure clarifying the earlier legislation was necessary.

"I believe resolving this controversy and making clear that every person feels welcome and respected in our state is best for Indiana," Pence said in a statement.

"Now that this is behind us, let's move forward together with a renewed commitment to the civility and respect that make this state great."