Sovereign Grand Master Rev William Anderson made the call as he addressed those gathered in the Co Armagh village of Loughgall for the institution's annual Last Saturday demonstration.
Around 17,000 members of the loyal order were involved across Northern Ireland, with major parades also taking place in Artigarvan, Dromore, Larne, Lisburn, and Moneymore.
It comes as the Stormont Assembly remains effectively collapsed amid DUP protest action over post-Brexit trading arrangements.
Unionists object to a trade border in the Irish Sea between Northern Ireland and Great Britain.
While the UK government and the European Union re-entered negotiations to agree the Windsor Framework earlier this year, DUP leader Sir Jeffrey Donaldson said he wants to see legislation to ensure Northern Ireland's place within the UK protected.
Rev Anderson said the Royal Black Preceptory's constitutional resolution called for the removal of the "continuing controls being exercised over citizens in Northern Ireland", and for the restoration of "full equal citizenship of the United Kingdom to all its citizens as set out in the Act of Union".
He called for Northern Ireland citizens to be freed "from the tyranny of persecution" being exercised by the European Union.
The resolution also referenced Northern Ireland's troubled past.
It sets out "there never was any justification for murder and violence" and refers to a "narrative that sets about the rewriting of such history".
Rev Anderson told the gathering: "Our hurt is being increased by those who are trying to rewrite their evil deeds of the past.
"Today, we need to remain resolute in our stand for those who are victims of violence of the past and ensure their stories are told accurately."