A South Boston veterans council, facing withering criticism, reversed course Friday and extended an unconditional invitation to the group of gay veterans it had barred from marching in the St. Patrick’s Day parade.

The move clears the way for OUTVETS, a group of LGBT veterans, to march in the March 19 parade with its rainbow banner and logo, a point of contention that the Allied War Veterans Council had cited when it voted Tuesday to reject the organization.

OUTVETS accepted the invitation Friday night. “We look forward to marching proudly on March 19 and honoring the service and sacrifice of those brave men and women who have sacrificed for our country,’’ the group said in a statement.

The war veterans council on Friday night agreed, by a vote of 11 to 0, to invite OUTVETS to the parade with no restrictions on the display of the rainbow flag, according to US Representative Stephen Lynch.

This second meeting was attended by younger veterans who “felt blindsided by this whole controversy and . . . wanted to make it right,” Lynch said.

“They’re committed to getting together and changing the way [the group] operates so we don’t have this every single year,” said Lynch, who had flown up from Washington to attend the meeting in hopes of resolving the standoff.

The developments Friday appear to resolve the latest chapter of a decades-old battle between the veterans council and gay organizations — a battle many thought was settled two years ago when the gay veterans group was allowed to march in the parade.

The fight once reached the US Supreme Court, which ruled in 1995 that the council could decide what groups marched in the parade.

The council’s 9-to-4 vote against OUTVETS on Tuesday had briefly rekindled the old fight. Nearly all of South Boston’s political leadership denounced that vote.

They were joined by Mayor Martin J. Walsh, Governor Charlie Baker, Senator Edward Markey, and others who said they would not march in the 116-year-old parade unless the vote was reversed.

The backlash extended to corporate sponsors — including Stop & Shop, Anheuser-Busch, the Dedham Institution for Savings, and Boston Scally Co. — who threatened or planned to withdraw their support.

The vote also raised questions about the makeup of the council, which has organized the parade since 1947. Some members who voted against OUTVETS either had not served in the military or did not live in South Boston.

The veterans council has about 25 members, traditionally drawn from each of the veterans posts in South Boston.

Its business is conducted in private, and individual votes are not disclosed, according to people familiar with the council.

In a quick-moving series of events, parade organizer Tim Duross, who sits on the council but is not a veteran, met Wednesday with OUTVETS leaders at the Omni Parker House in an impromptu attempt to reach a resolution.

Duross placed what he called a “letter of denial” on the table but withdrew the envelope as the meeting progressed, according to DeeDee Edmondson, a lawyer for the OUTVETS group.

On Thursday, about 25 to 30 veterans met in what a spokesman for City Council candidate Edward Flynn, a council member who voted for OUTVETS and had been trying to broker a deal, called a hopeful session.

Then, on Friday afternoon, OUTVETS received an e-mailed invitation, and the council formally agreed to invite the gay veterans group Friday night.

Before the invitation was extended and accepted Friday night, state Senator Linda Dorcena Forry, whose district includes South Boston, said she will not join the parade regardless.

“It is unacceptable to exclude anyone in our community. But the council has chosen to exclude the best of us: Veterans who have bravely served our country and put their lives on the line for our freedoms,” the senator said.

“I know this community does not share these ignorant beliefs. It is shameful that nine individuals would deny veterans the opportunity to march in a parade.”

City Councilor Tito Jackson, who is running for mayor, also said he will not march even if OUTVETS accepted the invitation.

“The nine narrow-minded committee members who voted to exclude OUTVETS . . . failed to meet the standards this nation and city pride themselves on — a deep and abiding commitment to treating every person with the dignity and respect they deserve,” Jackson said.

After Tuesday’s vote, state Representative Nick Collins of South Boston questioned whether all the council’s approximately 25 members knew that the OUTVETS application would be on the agenda.

City Councilor Michael Flaherty of South Boston also decried the ability of a small group to affect the neighborhood’s reputation, both locally and across the nation.

“What is clear is that the individuals making the decision to ban OUTVETS don’t have the interests of South Boston or our veterans in mind,” Flaherty said.

At least two veterans posts in South Boston have left the group in protest. Members of the Michael J. Perkins American Legion Post, composed primarily of veterans who served after Sept. 11, 2001, asked that the council remove “veterans” from its title “to prevent destroying the community good will that we and other South Boston veterans posts have worked hard to achieve.”

The Thomas J. Fitzgerald Veterans of Foreign Wars Post, which left the council last year after a parade application from Veterans for Peace was rejected, also denounced the move.

“Such restrictions deny veterans the opportunity to be honored for their service and sacrifice,” the Fitzgerald Post said in a statement.

Coleman Nee, a South Boston native and Marine veteran who served as state veterans secretary under Governor Deval Patrick, joined the chorus of criticism before the invitation was extended Friday.

“LGBTQ Americans have been serving this nation in uniform since General Washington’s army forced the British troops out of Boston,” Nee said.

Edmondson, the OUTVETS spokeswoman, said the group has received an outpouring of support and signed up more than 100 new members since the controversy erupted.

In addition to participating in the parade, OUTVETS raises funds for outreach to LGBT veterans and helps them understand and access their rights as veterans.