The commission was asked to provide a credible plan to restore public confidence after a court case highlighted mistakes in its handling of the parade.
The Northern Ireland secretary confirmed on Friday that he had received its response and would consider it over the weekend.
Speaking to BBC News NI, the Northern Ireland secretary said confidence in the commission had “taken quite a knock this week”, but that he was “not in the business of pulling the whole thing down”.
Sir Chris said he wanted to be assured there was a “coherent plan” which had the confidence of all communities.