Adams talks of 'new approach' to unionists
Sinn Féin's leader called for nationalists and republicans to adopt a new approach to "unlock unionist opposition to a new Ireland".
Gerry Adams made the comments at Sinn Féin's National United Ireland conference at the Waterfront Hall, Belfast, on Saturday.
He said it was important to "embrace" positive aspects of shared history.
It comes as talks to restore devolution continue at Stormont.
Mr Adams told the conference that recent election results at the assembly and Westminster showed a "deep political schism" in Northern Ireland.
He said: "Instead of concentrating on the negative aspects of our four centuries of shared history, I suggest that we embrace the areas of agreement and of co-operation; of good neighbourliness and the common good.
"Rarely have we lived through so much change in such a short space of time.
He added: "Our task must be to ensure that it is a shared future which looks after every citizen, and in which everyone accepts the right of the other to be Irish or British - to be unionist or nationalist or republican."
Mr Adams also said that the economic case for unification "will not on its own win some unionists over".
He therefore called for groups, including the Orange Order, to engage with Sinn Féin for further discussions.
"We need to address the future role of the Orange, its place in an agreed Ireland. Of course, that is a challenge also for the Orange and I invite their leaders once again to meet with Sinn Féin," he said.
"It is unacceptable for the Orange to refuse to meet at leadership level with our leadership.
"I have met with Orangemen as have other republicans.
"These have been useful and necessary engagements. They need to be built upon."