South Boston congressman Stephen F. Lynch says negotiations to allow a group of openly gay veterans to march in the city’s St. Patrick’s Day parade are still in progress.

Lynch, who has been marching in the parade since he was 4 years old, suggested the controversy could prompt him to skip this year’s event, and said there should be a way to allow the gay veterans to participate in the parade.

“If I think the veterans – all the veterans, including the gay veterans – have been treated fairly, then I’ll consider marching,” said Lynch, outside St Monica’s Church in South Boston on Saturday. “If I think that they have been treated unfairly, then I’ll probably decline the opportunity to march.”

A corned beef and cabbage luncheon was being held at the church. In attendance were several senior citizens already dressed in St Patrick’s Day green, according to the Boston Globe.

Also attending the event were parade organizers Philip J. Wuschke Jr. and John “Wacko” Hurley, who said again on Saturday that nothing had changed since they rejected MassEquality’s application to participate in the parade because organizers believed they had been misled by the statewide gay rights group.

MassEquality applied to march on behalf of 20 gay veterans, but parade organizers claim that the group has only been able to produce one veteran. MassEquality have disputed the claim that they had lied on the application and said they had plenty of veterans ready to march in the parade.

“I think there are several” gay veterans who want to march, Lynch said. “And even if there are only several, they should be allowed to march. There should be no numerical requirement. Even if there are only a handful, they should be recognized for their service. I think that’s only fair.”

The congressman said that he planned to meet with Wuschke, Hurley, MassEquality, and Mayor Martin J. Walsh.

The mayor, who has been trying to broker a compromise, arrived late to the luncheon on Saturday and walked up to the stage to address the crowd.

“I just want to tell you the reason why I’m late,” Walsh said, tongue in cheek. “President Obama called me on the way here and he asked me if I could call Wacko Hurley and the two of us would go to Russia and solve the problems they’re having.”

Walsh’s statement hinted at the bitter turn the parade negotiations took in the last week.

The controversy is a long-standing one. In the 1990s, the US Supreme Court ruled that although the parade was on public streets, it was a privately organized event protected by the First Amendment right to freedom of speech and therefore the government could not interfere to prevent organizers from prohibiting gays or any other group.

Parade organizers say that all political messages are barred from the parade and that gays and lesbians have always marched as individuals with other groups.

This year, at the mayor’s urging, parade organizers broke precedent and invited MassEquality to participate in the parade, with the condition that the group would be prohibited from wearing T-shirts or carrying signs that included references to sexual orientation. MassEquality rejected the condition.

The parade, which is organized by the Allied War Veterans Council,  posted a statement on its website last week saying that sponsors were being pressured to withhold support.

“We appreciate your continued support in lieu of the derogatory correspondence some of you received as a plot to circumvent donations greatly needed to finance this parade,” the statement read. “We have always tried to keep things on an even [keel] with regard to our changing community and political correctness . . . We’re not perfect, we’re a group of volunteers that love this parade.”

Walsh told reporters that he continued to hope for a compromise before the parade next Sunday.

“We’re in a period where hopefully both sides can take a step back and we can make something happen,” he said.