Ireland’s deputy prime minister has called for a generous and respectful conversation from all parties in the war of words over the Anglo-Irish border, warning that “reckless” shouting and sloganeering has consequences for the people who live in Northern Ireland.

Keeping the “hard-won peace” in the region was the only motivation in prioritising the Irish border in the Brexit negotiations, Simon Coveney told an audience of politicians, Whitehall officials and activists at a conference in Oxford.

Coveney had faced criticism from his political allies in Dublin over his dismissal of Jacob Rees-Mogg as “ill-informed about Ireland and the politics of the Brexit Irish border issue” after comments from the Tory MP saying that it might be an idea to “inspect” people crossing the Irish border after Brexit were revealed.

But he urged all parties to remember that the border was more than just trade – although the free flow of goods was an important by-product of the 1998 peace agreement.

In a keynote speech at the British-Irish Association conference in Oxford, Coveney said the flourishing of cross-border business and human interactions had reinforced peace and that this must be recognised by Brexiters who claim that the Irish border issue is overblown.

“Psychologically, it [peace] has transformed the landscape and allowed identity to breathe more freely. Protecting this precious achievement, a backbone to our hard-won peace, is the only motivation in prioritising Northern Ireland in the Brexit negotiations.

“These are real, not imagined, issues. And these are issues which must be addressed in the coming weeks if a positive outcome to the UK exit negotiations is to be secured,” he said.

“I know – because it has been said to me in the clearest of terms – that many in Northern Ireland find this discussion genuinely unnerving and even threatening,” he added.

In what will be seen as a sideswipe at Brexiters, he called for “generous and respectful conversation, not shouted slogans”.

“The danger of oversimplifying complex constitutional questions and choices without sufficient regard to the consequences is something all of us should be mindful of,” he added.

Earlier the leader of Fianna Fáil told the conference that relations between Dublin and London were the worst they had been in 30 years because of Brexit..

Micheál Martin, said the Irish taoiseach, Leo Varadkar, and his British counterpart, Theresa May, appeared to have no substantive working relationship and went for long periods without contact.

Martin’s party, like the Democratic Unionist party, is in a confidence-and-supply arrangement with Varadkar’s Fine Gael party. He said he was fully aware of the “constructive and chaotic nature” of politics in London but that the two governments still needed to develop and maintain a constructive relationship.

“The drift of recent years and the abrasive public relationship of the last year is very damaging.” He spoke of a seven-week period this year, during a crucial stage of the Brexit negotiations, when there was no contact between Varadkar and May.

Referring to previous Irish and British prime ministers, he said: “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.

British Prime Minister Tony Blair meets Irish Taoiseach Bertie Ahern in 2007.

Photograph: Lindsey Parnaby/EPA

“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,” he said.

He took a shot against at Coveney for criticising Rees Mogg’s historic comments, saying that while they referenced the worst aspects of the Troubles, they were made two years ago and Coveney should not have dignified them with a condemnatory tweet.

Martin went on to criticise Northern Ireland’s Democratic Unionist party for deliberately ignoring the duty of Dublin to protect the interests of that country’s nationalist population, who are neither represented in Westminster nor the local assembly because of the collapse of the power-sharing deal.

Sinn Féin has seven seats in Westminster but it does not take them because of its long-standing abstentionism policy.

“The attitude of the DUP to Dublin continues to ignore the will of the people of Northern Ireland concerning north-south relations,” he said.

However he reserved his sharpest words for Varadkar, claiming the taoiseach was misjudging cross-border relations and failing to develop a dialogue with unionists.

“When the taoiseach said last December, ‘It’s not my job to deliver the unionists’, he made a startling statement which none of his predecessors in the past three decades would have made,” he said.

Martin warned that 2018 was a grave moment in relations between the two islands and all leaders were responsible for mitigating the damage of Brexit.

Separately, Sinn Féin’s chairman said at the same event that the uncertainty being caused by Brexit was creating the right environment for a united Ireland.

Sinn Fein’s Declan Kearney said in a united Ireland, the party would act as a guarantor for the British identity and the unionist tradition. Photograph: Niall Carson/PA

Declan Kearney said that while unionists would find this anathema and the Conservative party,“unthinkable”, it was something to which many people aspired.

He said Sinn Féin, which for decades was associated with the IRA, would “act as a guarantor for the British identity and the unionist tradition”.

The party knew from first-hand experience that unionist and loyalist minorities would have to be supported in a united Ireland. “The 20% which would make up a new Ireland, who would not identify as Irish, must never feel the exclusion from society that was experienced by Irish citizens in the north under unionist rule,” he said.

In remarks that will rankle many union-supporting voters, Kearney said Sinn Féin recognised that “unionism needs to be persuaded that it can own a significant stake” within a united Ireland and republicans should remember they had a “responsibility” to welcome and cherish them.