With a bill (SB 1062) that would have allowed businesses to deny service based on their religious beliefs vetoed by Gov. Jan Brewer only hours before, the other proposal, HB 2481, is finding little immediate support, the Arizona Republic reported Thursday.
The bill, sponsored by Republican Rep. Steve Montenegro, prevents members of the clergy from being forced to "solemnize a marriage that is inconsistent with the minister's sincerely held religious beliefs."
Montenegro said he hopes the public outcry that doomed SB 1062 won't influence the vote on his legislation.
The bill is scheduled for consideration by the full House of Representatives but is finding little early support, the report said.
Republican Sen. Steve Yarbrough, who sponsored SB 1062, said he was unsure he would vote for a bill similar to his.
"I didn't come down here to hurt people," said Rep. Bob Robson, a Republican who voted for SB 1062 and then later said he regretted it. "There are times you take a vote, and then you feel queasy."
The Arizona constitution defines marriage as between a man and a woman.
Ministers, priests and rabbis are already exempt from being sued by people who feel they were wrongly denied marriage rites, said Tracey Stewart, regional director of the Anti-Defamation League.
The new bill would allow civil servants, including judges, to refuse to perform marriages that run against their religious beliefs. Such people are public employees and not religious figures, Stewart said.