Simon Coveney has warned Sinn Féin against using the problems Brexit creates for Northern Ireland to pursue an agenda of accelerated constitutional change leading to a united Ireland.

The Minister for Foreign Affairs told a meeting of the British-Irish Association (BIA) in Oxford that any conversation about constitutional change must be generous and respectful, without shouting and flag waving. “The challenges of these Brexit negotiations should never be twisted into tools for a constitutional agenda for Northern Ireland. To seek to do so would be reckless, risking increased division between communities in Northern Ireland and diverting focus from ensuring an EU-UK deal which best preserves our peace and normality,” he said.

Earlier, Sinn Féin chairman Declan Kearney told the conference that Brexit made a change in the political relations between Britain and Ireland unavoidable.

“The debate on Irish unity and the timing of a unity referendum have now moved centre-stage. Negative mismanagement of the Irish peace process and the Good Friday Agreement by successive British governments, and the particular pro-unionist bias of the Conservative government since 2010, must be replaced with a recognition that the transition towards Irish unity should begin,” he said.

Mr Kearney said that nationalists and republicans should acknowledge the fears of unionists but Mr Coveney said that those advocating Irish unity must show what they mean by tolerance and inclusivity and respect for those whose identity they do not share.

“Prove by your actions inside Northern Ireland that your vision of a shared future has room for those who are not like you. Help make Northern Ireland work, help make it a great place to live in, and work in, and raise a family in – whatever that family may look like – we come in all shapes and sizes these days. Work the institutions of the agreement – the inclusive, interlocking institutions of strands 1, 2 and 3 – to the full in a spirit of generosity and mutual respect. And abide by the spirit and the letter of the Good Friday Agreement. Seek to strengthen the three relationships it set out to repair – unionist and nationalist, North and South, east and west,” he said.

Established in 1972, the BIA’s annual conference brings together politicians, officials, academics, business people, faith leaders, writers and activists from Britain and both parts of Ireland. Its focus has traditionally been on Northern Ireland and the relationship between Britain and Ireland and discussions in recent years have been dominated by the impact of Brexit.

“It is inconceivable that Bertie Ahern and Tony Blair, or Brian Cowen and Gordon Brown would have gone seven weeks without talking at any time - let alone during a crisis.” Photograph: Gareth Chaney/Collins Fianna Fáil leader Micheál Martin sharply criticised the Government’s handling of relations with London and Belfast in the aftermath of Brexit, suggesting that the Taoiseach and the British prime minister “have no substantive working relationship”.

He said that although connections at an official level remained good, the political relationship between Dublin and London was at best poor.

“At the inter-governmental level relations are worse than at any time in at least the last 30 years. The Taoiseach and prime minister appear to have no substantive working relationship and go long periods without talking to each other. It is inconceivable that Bertie Ahern and Tony Blair, or Brian Cowen and Gordon Brown would have gone seven weeks without talking at any time – let alone during a crisis,” he said.

Mr Martin also accused the Taoiseach of failing to cultivate a dialogue with unionists as the Brexit vote has become an escalating point of division. He said the DUP and the Government were exchanging barbs through the media instead of seeking to improve North/South relations.