Ireland’s foreign minister has said the European Union’s most senior leaders have assured him Brexit talks will not move on to the next stage unless the UK gives greater guarantees over the Irish border.

Simon Coveney said Ireland did not need to use its veto as an EU member state to block progress in talks, because other European countries are in “complete solidarity” with Dublin over the issue.

It comes a week ahead of a key meeting between Theresa May and Jean-Claude Juncker and Michel Barnier, at which she is expected to try to secure their backing to move on from the first stage of talks and on to discussions of transition and trade.

Mr Coveney told Irish broadcaster RTE: “We don’t need to use a veto because we have complete solidarity on this issue with 26 other EU countries.

“It is clear to us that if there is not progress on the Irish border, we will not be moving onto phase two in December and that was reinforced to me as late as last Friday by very senior EU leaders.”

Ms May appears to have won some consensus on the issue of the UK’s divorce bill, having agreed to increase the amount Britain pays to settle its financial obligations, potentially up to £40bn. But the other two withdrawal issues – the Irish border and EU citizens’ rights are outstanding.

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Downing Street said on Monday that a meeting between Ms May and European Council President Donald Tusk had ended following “good progress” in negotiations, adding “there’s more to be done in a number of areas” and that talks continue to take place.

But Ireland has been pushing for more clarity on how the UK intends to avoid a land border between the Republic and Northern Ireland.

Dublin has said that if either the whole UK or just Northern Ireland remains in the single market and customs union, then there would be no problem with maintaining the current soft-border arrangements, but Downing Street has ruled them both out.

Any arrangement which appeared to give Northern Ireland a separate status to the rest of the UK would be strongly resisted by the Democratic Unionist Party party, whose 10 Westminster MPs are propping up Ms May’s Commons majority.

International Trade Secretary Liam Fox has said: “We don’t want there to be a hard border but the UK is going to be leaving the customs union and the single market.”

He told Sky News on Sunday: “We can’t come to a final answer to the Irish question until we get an idea of the end state.”

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Irish European affairs minister Helen McEntee has acknowledged that some of the final details of the border question would have to be dealt with in the next phase of Brexit talks, but said the UK must come forward with further proposals to achieve the aim of maintaining a soft border.

Meanwhile, Irish senator Neale Richmond, a European affairs spokesman for the Fine Gael party that leads the government, warned of violence if there is a return to a hard border.

He told the BBC’s Today programme: “There is paramilitary and criminal activity on both sides of the border at the moment, and indeed from both communities, and I come from an Irish community myself.

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“So to simply say that there’s no threat ... there is a threat, the PSNI [Police Service of Northern Ireland] and An Garda Siochana [the Republic’s police], have said there is a viable paramilitary threat to the peace process.

“You put up one watchtower, or put out one customs patrol, and they will be a target, and I would argue they would be attacked within a week of them going up.”