"Acceptance letter signed by Parade Organizer to allow @OutVets to march in 2017 parade," the group wrote on Twitter and Facebook.
It was not immediately clear what the acceptance letter entailed and whether OutVets would accept the invitation.
"OutVets is in receipt of a letter from the Allied War Veterans Council. We are actively reviewing it," the group wrote on Facebook.
The parade organizers, the Allied War Veterans Council of South Boston, did not respond to requests for comment.
Dan Magoon, who resigned as chief marshal of the parade in solidarity with OutVets, told CNN he was surprised by the organizers' short message.
"Quite honestly, from my view, the damage has been done," he said. "I still will be standing by OutVets and see what their decision process is. I'm still not participating in the parade."
The controversy began on Tuesday, when OutVets, which represents LGBT veterans, announced on Facebook that it had been denied
a spot in the March 19 parade.
In a message Thursday on its website, the council explained that OutVets had not been officially rejected from the parade, but it had not adhered to rules.
It said 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 Allied War Veterans Council had for years denied gay groups from marching in the parade, even winning a Supreme Court case
for the right to do so.
However, the council allowed OutVets to march in the parade in 2015 and 2016 in what seemed to be a breakthrough at the time.
Mayor Marty Walsh, as well as a number of other political leaders, promised to boycott the South Boston parade unless the decision was reversed.
Similarly, Anheuser-Busch said it was "re-evaluating" sponsorship
in the event, and CNN affiliate WBZ reported
that Stop & Shop had dropped its sponsorship as well.
OutVets and the Allied War Veterans Council met on Wednesday in an attempt to resolve the issue.
OutVets' Bryan Bishop said the meeting became "heated" when council officials asked him to change the group's rainbow logo, he told CNN. He refused to do so.
"This is not a political issue, this is an issue of discrimination against those who served," Bishop said.
Earlier on Friday, OutVets wrote on Facebook that it was "humbled and thankful" for support.
"It is equally overwhelming for the many supporters and champions for equality and inclusion who, once again, are challenged with the spectre of bigotry and discrimination," OutVets wrote. "We stand together! It is through adversity that we are made stronger."