The Irish government has said it is open to the possibility of a fresh proposal for a deal on the border issue, but will only consider a new plan if it is better than the one on the table.

The Irish finance minister, Paschal Donohoe, was speaking hours after Theresa May demanded the EU abandon its stance and “evolve its position” to include a guarantee there would be no border in the Irish Sea in the event of a no-deal Brexit.

“The only thing that could replace this current form of a backstop is, number one, something which is better, number two, something which is agreed, and number three, something that would be legally operable,” Donohoe told the Irish broadcaster RTÉ.

“The Irish government is very clear that the Irish backstop must be retained for any future agreement between the EU and the UK to be put in place.”

In a speech in Belfast, the UK prime minister said it was time for the EU to drop what she believes is its inflexible view on an Irish border solution to break the Brexit talks impasse.

She branded the EU’s proposal “unworkable” and repeated her assertion that a border down the Irish Sea was unacceptable to any British prime minister.

May said she was still committed to a backstop, or insurance policy, in the event of no deal, but it had to deliver the December joint report that sowed the seeds of the current disagreement by guaranting regulary alignment

north and south of the border.

The prime minister told an audience of business leaders in Belfast’s Waterfront building the UK government had “put an approach on the table which does precisely that” in the Brexit white paper – a goods-only proposal that would involve near-frictionless trade.

“It is now for the EU to respond. Not simply to fall back on to previous positions which have already been proven unworkable. But to evolve their position in kind,” she said.

Rajesh Rana, the president of the Belfast Chamber of Trade and Commerce, said: “That is a great deal if we can get it, but I don’t think the EU will allow it.

“If they give the UK a free-trade agreement involving a frictionless border without freedom of movement, other countries will just say they want that too.”

May used her speech to slap down hard Brexiters who said the Irish border was Dublin's problem not Britain. “We can’t solve it on our own, but nor can we wash our hands of any responsibility for it,” she said.

The EU’s 27 other member states had a chance to examine and respond to the white paper when its general council of ministers met in Brussels on Friday morning. They will also receive an update on the talks from the EU’s chief negotiator, Michel Barnier.

May’s decision to push back so strongly against the EU and Ireland’s demands for a backstop will fuel fears in Dublin she is backsliding on the joint agreement in December to secure insurance in the event of a no-deal Brexit.

Her opposition to a border in the Irish Sea was cemented on Monday when a last-minute amendment to the customs bill , tabled by the Labour MP Kate Hoey, was nodded through, making it illegal to have a barrier between Northern Ireland and Great Britain.

May is on a two-day visit to Ireland – her first to the Irish border. On Thursday, she spent two hours meeting business leaders at a pottery factory in the village of Belleek on the County Fermanagh and Co Donegal frontier, but did not take questions from reporters.

Before leaving the factory, May met Delma Käthner, a local woman, who told her she was “bionic”.

“She’s coped with so much,” Käthner said. “She has a terrible job. Just look at the way her shoulders are hunched. She has the whole weight of Brexit on her.”

Ireland’s taoiseach, Leo Varadkar, has expressed concern that the turmoil in the House of Commons suggested a withdrawal agreement would never be supported in Westminster, whatever the outcome of Brexit negotiations.