Lord Frost also called on Brussels chiefs to show more “common sense” to help find practical solutions to the problems arising from the Northern Ireland Protocol.
The minister spoke out after meeting business leaders in Northern Ireland to discuss the challenges they are facing following the UK’s departure from the EU.
A raft of protocol checks on goods at the ports in the province have sparked anger among unionists who feel Northern Ireland is being separated from the rest of the UK.
UK and EU officials are reportedly close to coming to an agreement on medicines to allow smoother passage of vital treatments from Great Britain and Northern Ireland.
But the two sides remain far apart on the majority of issues – including the possibility of an agri-food deal. The EU has suggested a Swiss-style veterinary agreement would eliminate 80 per cent of checks on goods.
But Lord Frost has rebuffed the offer, fearing that any agreement tying the UK to EU standards would damage the chances of a comprehensive free trade deal with the US.
“We are committed to working through the issues with the EU, to find a way forward and have been doing so intensively for the last few months,” Lord Frost said on Tuesday following his meetings.
He added: “We have proposed a range of solutions to the existing problems but progress is limited. We do think the EU needs to show more common sense and pragmatism.
“It is hard to see the protocol, as currently operating, could be sustainable for long and we continue to consider all other options.”
Lord Frost claimed Brussels “wants to treat the regulatory boundary in the Irish Sea as if it were like any other external border, despite the obligations of the protocol to facilitate trade”.
He also claimed EU Commission officials “aren’t always as clear about it as they could be” about the protection of the Good Friday Agreement.
The EU’s ambassador to the UK said the new claims by the new DUP leader Edwin Poots and others about the terrible damage done by the protocol in the wake of Brexit lacks “adherence to reality”.
Joao Vale de Almeida dismissed Mr Poots’ claims the trade arrangements are having a “devastating impact” and are causing “demonstrable harm to every individual in Northern Ireland”.
“First of all I don’t think those statements have adherence to reality,” Mr Vale de Almeida told the BBC on Tuesday. “The EU is politically, financially and emotionally, I would say, committed to peace and prosperity for everybody in Northern Ireland.
The diplomat added: “The protocol is not the problem. Brexit created the problem in Northern Ireland.”