Michelle O'Neill has urged a "sustainable compromise" in Northern Ireland through further dialogue.
She called for more respect for culture and identity.
Political talks to restore powersharing have been at an impasse for months over the issue.
The Sinn Fein vice president said she recognised people's right to be British, Irish or neither.
She met the Prince of Wales earlier this week.
Mrs O'Neill added: "We must reach a sustainable compromise through dialogue and agreement.
"Create a future where everyone feels they belong.
"Where our culture and identity is respected."
She addressed the opening night of Sinn Fein's ard fheis in Belfast on Friday.
"Instead of refighting the battles of the past we all - unionists and nationalists - need to have the humility to accept that we have conflicting narratives, conflicting histories and conflicting allegiances."
She said there was a clear requirement under the Good Friday Agreement on the part of the British and Irish Governments to ensure the equivalent standards of protection of rights which exist in all other parts of these islands and must exist in Northern Ireland too.
Stormont has not sat for months in a row over the Irish language.
Mrs O'Neill told decision-makers in Dublin and London: "You must convene the British-Irish Intergovernmental Conference without delay, and determine how you as the joint stewards of the peace process will remove the obstacles to powersharing."
She accused the DUP of putting their "self-serving" pact with the Tory party at Westminster before people's interests in Northern Ireland in defeating Brexit.
"They're living in a fool's paradise.
"They blindly prop up Theresa May, who is preoccupied with negotiating with her own cabinet rather than the EU.
"Britain is divided. But in Ireland we are united.
"We will not be collateral damage as a result of the reckless Tory/DUP Brexit agenda."
The DUP has secured extra funding for Northern Ireland public services through its deal to support the Conservatives in key votes.
It wants to avoid a border in the Irish Sea after Brexit so is keen to ensure Northern Ireland does not diverge from the rest of the UK following the withdrawal.
Sinn Fein wants to see Northern Ireland remain in the EU Customs Union.