Ireland’s foreign minister, Simon Coveney, has told the Conservative party that getting rid of Theresa May will not remove the need for a Brexit backstop for the Northern Ireland border.

Speaking on BBC Radio 4’s Today programme he pointed out that a no-deal Brexit, which some of May’s potential successors have been considering, would require checks on goods travelling across the border.

This reality would not change whoever the Conservatives chose as their new leader, Coveney said, and he urged the party to back May’s withdrawal bill.

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He said: “Without a [withdrawal] deal, then we essentially have Northern Ireland as part of the United Kingdom, in a different customs union and a different single market, to the Republic of Ireland, which will be part of the EU customs union and single market. And if goods travel from one customs area to another, from one single market to another, there will need to be checks somewhere.”

Asked what would happen if May’s successor was determined to scrap the backstop arrangement in the withdrawal agreement, Coveney said: “These realities don’t change. This is not a personality-based issue. It is an evidence-based issue. Within the current withdrawal agreement that’s available … there are the flexibilities there to look at alternative arrangements to the backstop if they work. If they stand up, they can replace the backstop.

“But we have to move forward on the basis of knowing that we are not going to see the kind of damage done on the island of Ireland, that the imposition of a border would result in.”

Coveney also signalled his determination to see power sharing restored to Northern Ireland within weeks and said the killing of the journalist Lyra McKee was a warning of what could happen in a political vacuum.

He insisted there had been significant progress in talks about restoring a devolved assembly since politicians of all sides were criticised at the funeral address for McKee last month.

“There is an acceptance amongst all political parties in Northern Ireland – nationalist and unionists and neither – that they have an obligation to try and make this process work,” the tánaiste (deputy prime minister) told Today.

“The British and Irish governments will work closely together to try and do some of the heavy lifting with the political parties that can change this within weeks, not months.”

Coveney added: “We’ve seen in the killing of Lyra McKee, what happens in a vacuum where politics isn’t working, and we need to correct that.”

When it was put to him that there was little sign of progress since the funeral, Coveney said: “There’s been more than some movement and when positive things happen, it’s important to recognise them. We started a formal talks process and, on Wednesday, we had what’s called a British-Irish intergovernmental conference here in London. Yesterday and again today, we are seeing work streams, that all of the parties in Northern Ireland are part of.”

He also spelled out the urgency for restoring power sharing after more than two years.

Coveney said: “There are many issues that need political decisions that don’t have them. Northern Ireland society is suffering because of that, and particularly in the context of the stresses and strains of Brexit. And the need for contingency planning and so on. The inability for Northern Ireland to make decisions for itself is something that we all have an obligation to correct.”