By Scott Malone

BOSTON (Reuters) - Organizers of Boston's St. Patrick's Day Parade denied on Thursday that they told a gay veterans' group its members could not march openly in one of the largest U.S. celebrations of the holiday and accused the group of breaking parade rules.

The veterans' group, OUTVETS, said late on Tuesday it had been informed by parade organizers it would be excluded from this year's parade, rekindling a decades-long fight over inclusion that had looked settled in 2015 when the group was first allowed to march.

"OUTVETS has not been officially notified that they will not be allowed to march in the Parade," the Allied War Veterans Council, which organizes the 116-year-old event honoring Ireland's patron saint, said in a statement posted to its website on Thursday.

"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.

It said the group had not filed its application to march on time and added that since OUTVETS' Tuesday statement, parade organizers had "received numerous vitriolic and hate-filled emails."

Parade officials did not respond to requests for further comment.

Brian Bishop, director of the gay veterans' group, laughed when a reporter described the statement to him.

"If that's what they're saying, hey, great. All I know is the phone call that I got on Tuesday night said that we were being excluded," said Bishop. "We thought that we had gotten through this already."

The move by parade organizers to exclude the group drew criticism from political leaders in Massachusetts, which was the first U.S. state to legalize gay marriage more than a decade ago. Boston Mayor Marty Walsh, a Democrat, and Governor Charlie Baker, a Republican, are among the politicians who have said they will skip the March 19 event if the gay veterans' group is excluded.

Parade organizers long cited their Roman Catholic faith as a reason for excluding openly gay participants, as the Catholic Church teaches that homosexual conduct is sinful. They said on Thursday that allowing openly gay marchers had prompted other Catholic groups that had long participated in the march to bow out.

New York's parade also long excluded openly gay marchers, but both organizations in 2015 allowed gay groups to participate after major sponsors dropped their funding of the events.

(Reporting by Scott Malone; Editing by Peter Cooney)