ST. PAUL — The leader of the group lobbying for gay marriage at Minnesota’s Capitol said Wednesday he supports a proposed change to the bill that could make it easier for Republicans to support.

The House is scheduled to debate and vote Thursday on the bill to legalize gay marriage in Minnesota. An amendment posted Wednesday from GOP Rep. David Fitzsimmons reframes the proposed changes to wording in Minnesota’s marriage laws, swapping in the term “civil marriage” in all instances whether couples are of the same or opposite genders.

Richard Carlbom, director of Minnesotans United, the lobby group pushing for gay marriage, told The Associated Press that the group has agreed to back the amendment meant to guarantee that religious organizations couldn’t be fined, punished or stripped of special status for refusing to perform gay marriages.

The group’s support is critical for the success of the amendment, which has the potential to draw Republican support for the bill. A religious protection clause had been in the bill, but some Republicans thought it wasn’t strong enough.

“It just makes it clear we’re talking about civil marriage, not religious,” Carlbom said. He said it’s superior to another Republican proposal, to allow civil unions, which gay marriage supporters had criticized as creating as “separate but equal.”

Carlbom urged House and Senate gay marriage supporters to accept the GOP changes. Two key House Democrats — Rep. Karen Clark, the House sponsor of the bill, and Majority Leader Erin Murphy — said they also support the amendment.

What wasn’t immediately clear was whether the gay marriage bill would net Republican votes if the amendment passes,. So far, no House Republicans has committed to voting for the bill.

Fitzsimmons couldn’t immediately be reached for comment. Rep. Joe Hoppe of Chanhassen, a Republican who supports civil unions, said he was at least open to backing the bill if Fitzsimmons’ proposed changes are successful.

If the House passes the bill, it would be sent to the Senate for a vote that could come as early as Saturday. Democratic Gov. Mark Dayton has vowed to sign the bill, which would allow gay marriages to start happening on Aug. 1.