The Orange Order claims it has been "demonised" after the murders of the three Quinn brothers during the Drumcree standoff in July.
In an unprecedented step, the order has published a number of information sheets setting out its position on the killings, and has stated its commitment to the Northern Ireland Assembly.
The order pledged its support for the power-sharing government, which is due to reconvene in September, and stressed that the Drumcree standoff was not orchestrated to bring it down.
It added that it was committed to working in the proposed civic structures outlined in the Belfast Agreement.
"The democratic decision taken by the referendum is recognised by the Orange Institution, and we intend to play our part in proposed civic structures.
"The Grand Orange Lodge of Ireland fully supports the work of the new Northern Ireland Assembly in its task of underpinning the future peace and stability of this province within the United Kingdom for the benefit of all its citizens," the order stated.
A leading Orangeman, Mr David McNarry, said Portadown Orangemen "received the wholehearted backing of many" supporters of the Belfast Agreement.
The order denied that its members and the Drumcree standoff had any direct responsibility for the murder of the Quinn children.
Richard Quinn and his brothers, Mark and Jason, died in an arson attack on their Ballymoney home in Co Antrim during the Orange protest in Portadown, Co Armagh.
The order claimed the Orangemen at Drumcree or those supporting them "could not be held to account" for the murders.
Ultimate responsibility rested with whoever started the fire, and the order accused others of exploiting the deaths for propaganda purposes.
"If sectarian hatred was the reason for the murders, then society must shoulder the responsibility. The Orange Order is not the scapegoat for society's shortcomings.
"Murder and violence are most definitely not the stock-in-trade of the Orange Institution," the statement added.