A group of gay and transgender military veterans barred from marching in the St. Patrick’s Day Parade in South Boston will now be allowed to participate in the March 19 event.

The parade organizers, the Allied War Veterans Council of South Boston, voted unanimously late Friday to reverse their decision made on Tuesday to exclude the group, OutVets, which had marched in the event the past two years. OutVets had been given two reasons for being excluded — its application was late and the rainbow in the group’s logo, worn on jackets, was in violation of the parade’s code of conduct.

But after the organizers voted 9 to 4 to exclude OutVets, council members came under increasing pressure to reconsider. Top politicians in the state, including the governor, Charlie Baker, and the mayor of Boston, Martin J. Walsh, announced they would skip the parade.

The reversal came during a meeting arranged by Representative Stephen F. Lynch, Democrat of Massachusetts, and other elected officials at the V.F.W. Post 561 in South Boston. After the meeting, members of the Allied War Veterans Council said the change was the right decision.