Organizers of South Boston's annual St. Patrick's Day parade say a gay veterans group has not been "officially notified" that it cannot march, but that the group had been informed that its rainbow flag was in violation of the parade's code of conduct.

In a press release issued Thursday to address "rumors and accusations," the Allied War Veterans Council, which runs the parade, said that the gay veterans group, OutVets, "was informed that our Code of Conduct prohibits 'the advertisement or display of one’s sexual orientation,' and that the 'rainbow' flag on its banners and logo was in violation of this rule."

The council added in the release: "The question at hand is not one of inclusion or discrimination."

On Wednesday, OutVets said it had been denied a spot in this year's event -- just two years after parade organizers first allowed the veterans to march, and following a decades-long battle to be included.

OutVets attorney Dee Dee Edmondson told WBUR that the emblem was never a problem when the group marched in the last two parades, and it won't abandon it now.

"What they are really saying is, 'We don't want you to be gay in our parade, we want you to look like us...act like us...just don't be gay...take away the rainbow flag,' " Edmondson said. "We did ask if all the rainbows that go to the pot of gold with Saint Patrick are going to be removed too, and they said no, those are fine."

Wednesday's news was met with condemnation from many, including Allied War Veteran Council member and Boston City Council candidate Edward Flynn.

"As a 25-year United States Navy veteran, I supported OUTVETS in 2014 and did so again this week," he said in a statement. "I remain hopeful that my colleagues on the Council will correct this situation and join me in voting for inclusion. If this vote does not affirm their right to march in the parade I will not be marching."

The Allied War Veterans Council will meet Friday to hold a second vote on whether to allow OutVets to join the procession. It said in its news release Thursday that OutVets also did not submit its parade application before the deadline.

"The Council sometimes makes exceptions for late applicants," the release said, "but in order for Outvets to be considered for participation in the Parade, the Organization must address the Code of Conduct violation."

On Wednesday, Dan Magoon, this year's parade chief marshal, stepped down from his post to show his support for OutVets' inclusion, and a number of politicians, including Boston Mayor Marty Walsh, Gov. Charlie Baker and Rep. Seth Moulton — himself a vet — said they too won't march if OutVets is left out.

"I hate to say this, it's discrimination, that's all I can say, it's discriminatory," Walsh told WBUR Wednesday. "We are one Boston. We are so beyond this conversation."

In response to OutVets' rejection, grocery store chain Stop & Shop announced Wednesday that it is pulling its sponsorship of the parade. Brewing company and parade funder Anheuser-Busch said it too is debating walking out on the event.

With reporting by WBUR's Lisa Creamer and Paul Connearney