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Boston • A gay rights advocacy group said Monday that it is pushing for gay people to be allowed to march "openly and honestly" in Boston's St. Patrick's Day parade, but an agreement has not been reached with parade organizers.

It appeared Saturday as if Boston Mayor Martin Walsh had brokered a deal between MassEquality and parade organizers to allow gay military veterans to march under the group's banner, but the deal was not finalized even after both sides met a day later. The sticking point is whether and how members of the group can identify themselves in the parade.

"LGBT people need to be able to identify themselves as LGBT people. It's as simple as that. There's a lot of ways that can be done, and that is a conversation we're having now with organizers," MassEquality Executive Director Kara Coredini said Monday.

"I'm hopeful that we'll get to a place where we'll be marching in the parade, but we're not there yet," she said.

Tim Duross, the parade coordinator, said the two sides have reached a stalemate. He said the parade sponsor, the South Boston Allied War Veterans Council, is willing to allow the gay veterans to march with the MassEquality banner, but said they are insisting that they be able to carry signs and wear T-shirts identifying themselves as gay. He said organizers want the focus of the parade to be on celebrating St. Patrick's Day.

"The fact that they need to identify themselves as openly gay veterans is kind of where the stalemate lies. I don't know why that's so important in this parade," Duross said.

"We are not planning romances here. We are just putting on a parade."

Duross said the parade sponsors plan to discuss the MassEquality request during a meeting Tuesday night.

The mayor's office did not immediately return a call seeking comment.

The parade sponsors, the South Boston Allied War Veterans Council, have had a history of turning away organized gay groups.

In 1992 and 1993, state courts forced the group to allow the Irish-American Gay, Lesbian and Bisexual Group of Boston to march in the parade. In 1994, the group canceled the parade rather than allow the gay group to participate.

In 1995, the sponsors said the parade would commemorate the role of traditional families in Irish history and protest the earlier court rulings. The same year, the U.S. Supreme Court ruled that Massachusetts courts had violated the parade sponsors' First Amendment rights when they forced them to allow the gay group to march.

Meanwhile, the Immaculate Heart of Mary School, near Worcester, said Monday that its band will not march in this year's parade because of the participation of MassEquality.

"We don't want to appear that we are condoning the homosexual lifestyle," said Brother Thomas Dalton, principal of the Catholic, K-12 school in Harvard.

Dalton said the school has participated in the parade for 24 years, through its marching band and a float depicting Saint Patrick blessing the crowds.