Mrs Ruth Patterson a DUP Councillor in Belfast apparently made the remarks on Facebook.
It was in reply to a post from someone else foreseeing an imaginary attack on the parade in which several people including Sinn Féin figures are killed.
A response under Ruth Patterson’s profile asked: “… Who cares how we would be judged, we would have done a great service to Northern Ireland and the world.”
Asked by the BBC if she had written those words, Mrs Patterson said “That was on a private page. I can’t comment on that at the moment.”