Theresa Villiers has set out her vision of a shared future for Northern Ireland, including the prospect of a move to a political system with a government and opposition.
The Northern Ireland Secretary said education and housing remained too segregated and warned that the “costs of division remain far too high”.
Ms Villiers also used her speech to the Conservative Party conference to send a message to those who continued to be involved in violence that “you will not succeed”.
She told activists in Birmingham: “A key priority has to be building a genuinely shared society by tackling sectarianism and overcoming the divisions which still persist within Northern Ireland.
“For all the progress that’s been made, too many children are educated completely separately, too much public housing remains segregated and the costs of division remain far too high.”
She backed the work carried out by the Northern Ireland Executive on shared education, encouraging better links between schools to “increase friendship and understanding across long-standing community divides”.
Ms Villiers added: “When they take the difficult decisions needed to make progress, the UK Government stands ready to back them.
“And yes there may be times when the Government and the Executive don’t agree on the pace of change. But when that happens I hope it can be done in a constructive and grown up way, a sign that politics is moving on and the relationship between Westminster and Stormont is both mature and evolving.
“And as politics in Northern Ireland move forward, it’s only right that we look at how the devolved institutions might be made more effective.
“So we’ve been consulting on issues such as the size of the Assembly and ending dual mandates - and make no mistake, we will end dual mandates and double jobbing.
“We’ve also used this process to give people the chance to have their say on whether, over time, we could move to a more normal system which allows for a government and an opposition.”
But she moved to reassure people in Northern Ireland that “any changes can only come about on the basis of widespread agreement among the parties and across the community”.
“They must be consistent with power sharing and ensure that the rights of both main traditions are respected. Stability in Northern Ireland has been hard won and this Government will not push forward with anything which puts that at risk.”
The political process would not be derailed by those who continued to use violence, she added.
“They act in defiance of the will of the people of Ireland - North and South - who voted in such overwhelming numbers for the current settlement.
“I have a clear and simple message for those terrorists: you will not succeed. The future of Northern Ireland will only ever be decided by democracy and by consent, never by violence.”