Northern Ireland Protocol: No breakthrough after latest talks
Lord Frost and his EU counterpart Maros Sefcovic will meet next week after the latest talks on the Northern Ireland Protocol failed to produce agreement.
The UK wants fundamental changes to the protocol's operation and governance.
The EU has proposed a more modest package of measures which would reduce its practical impact.
A UK spokesman said: "While there is some overlap between our positions on a subset of issues, the gaps between us remain substantial."
He added: "Our position remains that substantial changes to the protocol will be needed if we are to find a sustainable solution that works in the best interests of Northern Ireland."
An EU spokesman said: "It is now essential to find common ground between the EU and UK's respective positions.
"We owe it to the people of Northern Ireland to find stable solutions as soon as possible."
The protocol is the special Brexit deal which prevents a hard Irish border by keeping Northern Ireland inside the EU's single market for goods.
That also creates a new trade border between Northern Ireland and the rest of the UK, something the EU accepts is causing difficulties for many businesses.
Unionist politicians say the arrangement undermines Northern Ireland's place in the UK.
Meanwhile the BBC has seen a European Commission briefing for member states which says the role of the European Court of Justice (ECJ) in the protocol is not up for discussion.
The UK wants the ECJ removed from any role in dispute resolution.
The commission briefing says that as the protocol involves the application of EU law, the ECJ must be involved.
On Tuesday, Brexit Minister Lord Frost said the role of the ECJ was not the only problem and the protocol meant "far too much EU law" applied in Northern Ireland.
EU and UK officials will continue talks next week before Lord Frost and Mr Sefcovic meet in Brussels on Friday.