The organizer of the annual South Boston St. Patrick’s Day Parade today opened the door to allowing a gay veterans group to ultimately march in the event despite a vote last night to bar it, a decision that sparked severe backlash from the city and state’s top leaders.

Tim Duross, emerging from a meeting with the head of OutVets, said the group’s rejection is not “official” despite last night’s 9-4 vote, and that he planned to reopen discussions with members of the South Boston Allied War Veterans Council.

“I would like to see everyone in the parade,” Duross told the Herald by phone. Duross defended the vote, saying it wasn’t based on “discrimination” but concerns that OutVets had violated parade rules, which he said bars “portrayal of sexuality.” The issue, he said, centers on the inclusion of a rainbow flag in the OutVets’ logo.

“I’m going to go back to the council and see if we can resolve something,” he said. “I need to be sure that everyone is on the same page. If everyone abides by our rules and they’re not outlandish, I think we can all have a great parade.”

But Bryan Bishop, director of OutVets, said he was told his group could march — if it removes the flag from the logo, something he is vehemently against. Bishop said parade organizers are planning an emergency meeting for later this week to discuss the situation.

“It’s not happening — It’s like taking the stars off the American flag,” Bishop said of changing the logo, adding the group ultimately won’t march if its invite comes with such conditions. “The only way this is going to fly is a 100 percent open opportunity for us to march with no conditions — unconditional acceptance into the parade. Anything less than that, it’s a no go.”

Earlier today both Gov. Charlie Baker and Boston Mayor Martin J. Walsh said they will skip the annual parade in South Boston if OutVets didn’t march — and U.S. Congressman Stephen Lynch said he will try to “resolve” the issue.

“I am going to try to resolve this. I think I will be able to. There is no reason for this,” Lynch, who represents South Boston, told Adriana Cohen and John Sapochetti on Herald Radio this afternoon. “These young men and women served this country and they have a right to march like any other veteran. It’s disheartening to see an attempt to treat them differently.

“If I can’t resolve it,” the congressman added. “I regret I cannot accept the invitation to march, but that’s the way it’s got to be.”

Bryan Bishop, the director of OutVets, said he hasn’t been given a concrete reason why the application was denied, other than a claim that the group missed a mid-February deadline to apply. But Bishop said there was no deadline listed on the application, nor was he aware of one for past years.

OutVets said on their Facebook page that the reason for the denial is unclear, but “one can only assume it’s because we are LGBTQ.”

The South Boston Allied War Veterans Council, the parade’s organizer, voted 9-4 last night to keep the group out of the March 19 parade.

Daniel Magoon, the executive director of Massachusetts Fallen Heroes, had been slated to serve as the parade’s chief marshal, but said he will not after the decision to exclude OutVets.

“I have worked hard over the years to support returning veterans and their families,” Magooon said in a statement. “We have fought battles across this city, state, and country in regards to veterans rights, benefits, employment, mental health, discriminatory practices and may other significant areas important to our veterans. To be a part (of) a parade exluding OutVets does not coincide with the work I do advocating for all veterans.”

The vote swiftly spurred an outcry by lawmakers.

In a statement, Walsh said: “I will not tolerate discrimination in our city of any form. We are one Boston, which means we are a fully inclusive city. I will not be marching in the parade unless this is resolved. Anyone who values what our city stands for should do the same.”

However, Walsh said there is nothing the city can do to force the inclusion of OutVets and said he would not “go down the route” of pulling the permit for the parade, but held fast on his promise to boycott.

“I would suggest other people in the parade don’t march in the parade,” Walsh said.

Asked whether he would skip the parade due to the exclusion of OutVets, Baker told reporters, “my view on this one is pretty simple, which is it’s a veteran’s parade. Veterans groups should be allowed to march in the parade… If veteran’s groups aren’t allowed to march in that parade for whatever reason, then I’ll probably do something else.”

The governor said he spent most of the past weekend with the families and friends of two active duty service members — one from the Coast Guard and one from the Army — who were killed last week.

“That word, ‘veteran’ to me, it approaches holy,” the governor said. “The idea that we would restrict the opportunity for men and women who put on that uniform, knowing full well they could put themselves in harm’s way, and deny them an opportunity to march in a parade that’s about celebrating veterans doesn’t make any sense to me.”

U.S. Rep. Seth Moulton, a Marine Corps veteran, called for a complete boycott of the parade.

“It is outrageous and disgraceful that a group by the name of Allied War Veterans would decide to ban OUTVETS from marching in this year’s St. Patrick’s Day Parade,” the Salem Democrat said in a statement. “Let’s just be clear, these are men and women who courageously put their lives on the line for our country. They deserve our respect just as much as anyone, and if this decision is not reversed immediately, I would encourage anybody who supports freedom, equality, and the service of our veterans no matter who they are, to boycott this parade.”

The parade has been the subject of controversy for decades.

In 1995, organizers won a Supreme Court ruling that let the South Boston Allied War Veterans Council exclude gay groups on First Amendment grounds. The groups were banned until 2015, when, with Walsh’s backing, OutVets was first allowed to join the route.

“This argument is so old that I can’t even believe we are having this conversation right now about the parade, this is uncalled for,” Walsh told reporters this afternoon.

“The issue is they don’t want us there,” said Bishop, who called the parade council an “organization that has outlived its usefulness.”

“If we want to have a St. Patrick’s Day celebration, it should be downtown, the city should run it and it should be a fully open and inclusive event,” Bishop said. “Basically this is unacceptable.”

Referencing the 9-4 council vote, the mayor said, “I am not even blaming the veterans, it’s nine people who voted discriminatorily in not allowing OutVets to march. They’ve marched the last 2 years, it’s been a great parade, it’s been a very peaceful parade. Unfortunately these are nine individuals who are putting themselves before anybody and I am hoping the veterans’ organization can overturn this and do the right thing.”

Walsh said he believes the vote of the council does not reflect the opinions of most members of the South Boston Allied War Veterans Council and the turnout for the vote was low. Some of the members who voted to exclude OutVets are not Boston residents, Walsh said, reiterating he will not march in the parade if OutVets is excluded.

Asked what he thought was driving the decision of the nine members who voted against including the gay veterans group, Walsh said, “I hate to say this, it’s discrimination, that’s all I can say, it’s discrimination…this is so wrong what happened here.”