The EU has launched a direct sales pitch to Northern Ireland businesses in an attempt to drive a wedge between the Democratic Unionist party and Theresa May over the backstop solution for the Irish border in Brexit negotiations.

As the rhetoric from Belfast intensifies and the DUP restates its opposition to any checks on trade between Britain and Northern Ireland, Sabine Weyand, the deputy to the chief negotiator, Michel Barnier, told a delegation of Northern Irish business leaders invited to Brussels this week that the deal on the table was “the best the EU has ever offered any country in the world”.

She told them it would give Northern Ireland businesses “unfettered access” to both the single market and Britain and is a “really big deal” for the EU, according to those present.

The best of both worlds narrative is part of a fresh offensive by the EU to try to avert a no-deal by appealing directly to the hearts and minds of Northern Ireland interests.

It comes as Brexit negotiations enter what is being referred to as a “tunnel phase”, with no publication of the British or EU position on the backstop to be published until it is agreed.

But the DUP has expressed concern that May has “swallowed” an “EU confidence trick” and has been persuaded by arguments that checks on goods destined for Ireland in British ports and premises would not constitute a border in the Irish Sea.

However, business leaders in Belfast said they believed the EU deal could be a “life jacket” for the region and avert a no-deal disaster.

“They said they think this is an amazing deal you are getting, something nobody else in the world has even been offered,” said Seamus Leheny, the director of policy at the Freight Transport Association of Northern Ireland, who was at the meeting.

EU sources have separately expressed deep frustration that their message is being drowned out by narratives in Belfast and London. “We have been incredibly flexible, we are breaking our single market rules just because of the unique position of Northern Ireland. This has never been offered to anyone else and will not be offered in the future,” said a source.

The dozen delegates from Northern Ireland business also said the deal would allow Northern Ireland to continue to avail of trade deals including the recent one struck with Japan, something Britain may not be able to seal until long after 2020.

“It’s a life jacket to us. They are offering us unfettered access to both the EU and the UK markets,” said Leheny. “They are going on the offensive because they think this message is getting blocked out by the London and Belfast [DUP] narrative.”

“The DUP was always seen as the party of business, and if the business community says we need a backstop solution, maybe they think it will be harder for the DUP to block a deal,” said Leheny.

The Northern Ireland Retail Consortium (NIRC), which also attended the meeting, said the deal on the table was uniquely beneficial to Northern Ireland’s economy, which would suffer disproportionately from Brexit.

The DUP has warned it will vote against any deal that involves checks between Northern Ireland and Britain, with Sammy Wilson, the DUP MP for East Antrim, accusing the EU of performing a “confidence trick” on May.

Aodhán Connolly, the director of the NIRC, said: “The offer the EU has made to Northern Ireland is uniquely beneficial.”

He said no deal would “quite simply be a disaster for business in Northern Ireland”, where consumers already have half the disposable income of households in Britain.

Business leaders in Northern Ireland say the trade between the two islands is dominated by 88 large companies such as Guinness, but the impact of Brexit on the border will be felt by small businesses.

“Most of the trade between north and south is by small traders, 98% of firms in Northern Ireland employ fewer than 20 people, 95% employ fewer than 10 people. We are a small economy and one wrong push on the pedal could significantly impact our economy,” said Tina McKenzie, the chair of the policy forum for the Federation of Small Businesses in Northern Ireland.