Lord Frost said the UK wants to “secure a solution based on consensus”, after his Cabinet colleague Michael Gove earlier appeared to row back on the threat to trigger Article 16.
Negotiations appear to be gathering pace, with Mr Sefcovic welcoming the “change in tone” from the UK and calling for “joint tangible solutions” to be found within the framework of the protocol.
Lord Frost described talks as “intensive and constructive”, adding: “There is the potential to generate some momentum in our discussions.”
But he warned “significant gaps remain across most issues”, and said a “significant change from the current situation” is required.
He said the option of triggering Article 16, which would suspend elements of the post-Brexit arrangements, remains an option if a solution cannot be found.
“On medicines, there has been progress but agreement has not been reached,” he said. “Any acceptable solution needs to ensure that medicines are available at the same time and on the same basis across the whole of the UK.
“We have not yet made substantive progress on the fundamental customs and SPS issues relating to goods moving from Great Britain to Northern Ireland.
“A durable solution here requires goods to be able to move essentially freely into Northern Ireland when both sides agree that they are remaining in Northern Ireland.”
Mr Sefcovic said it is time to switch to “a result-oriented mode” and to “deliver on the issues” raised by stakeholders in Northern Ireland.
“It is essential that the recent change in tone now leads to joint tangible solutions in the framework of the protocol,” he said.
He added there is a “genuine urgency” to resolve the issues of medicines flowing from Great Britain into Northern Ireland.
“We now need to press on and get this crucial issue across the line,” he said.
“This is a real test of political goodwill. The EU, for its part, is confident that our proposed solution, addressing all concerns raised by industry, would bring much needed clarity and foster a positive political momentum.
“On customs, there has been initial useful engagement at technical level. These discussions, which aim to significantly reduce, not to eliminate, customs processes, should be pursued.”
But he called for more movement from the UK on the issue of sanitary and physiosanitary checks.
Mr Sefcovic said: “The EU-proposed solution would lead to a very significant simplification of certification and a reduction in checks. Identity and physical checks would be reduced by around 80% compared to the checks currently required.”
Earlier, Mr Gove expressed confidence that talks can progress without the need for the UK to trigger Article 16.
Speaking at the British-Irish Council summit in Cardiff, Mr Gove said: “I do believe that there is a constructive approach that’s being taken by the Commission and Lord Frost has signalled that while, of course, it’s always possible that Article 16 may require to be invoked, we’re confident that we’ll be able to make progress without it.”
But he declined to rule out the option completely.
“I hope that we won’t need to trigger Article 16, for reasons that will be well understood, but we reserve the right to do so if we believe that changes which are required on the ground in Northern Ireland have not been made,” he said.
Irish premier Micheal Martin said he believes there is “a genuine desire” on all sides to resolve the protocol dispute without the use of Article 16.
He told the summit: “I believe that in the discussions I’ve had now over the last while, that there is a genuine desire on all sides to get this resolved through negotiation, and through the avoidance of triggering any particular mechanisms within the Withdrawal Agreement.”
Prior to the latest talks with Lord Frost, Mr Sefcovic said new measures on the protocol will create an “express line” on trade between Northern Ireland and Great Britain, resulting in a “win-win situation” for all.
He said the bloc will offer to permanently slash customs paperwork by 50%, along with the removal of up to 80% of checks.
Mr Sefcovic was speaking at the Brexit Institute at Dublin City University on Friday, immediately before the crunch talks with his counterpart.
He called on the UK to “reciprocate” and welcomed the recent “change in tone” in talks.
Mr Sefcovic said the “comprehensive long-term solution” that would see “further facilitation and simplification” of customs checks will result in a “50% permanent reduction in existing paperwork”.
He added: “These measures would create a type of express line, which would substantially facilitate trade between all parties, a win-win situation for all.
“It is a unique and completely new model for how goods can be moved from Great Britain to Northern Ireland, one that will strengthen opportunities for people and businesses alike.
“It will make the application of the protocol more transparent while at the same time respecting the UK’s constitutional order.
“A website will also be set up to show in a clear and comprehensive way the EU legislation applicable in Northern Ireland.”
However, Mr Sefcovic has warned the post-Brexit trade deal is “intrinsically linked” to settling the Withdrawal Agreement, which includes the Northern Ireland Protocol.
“Settling the divorce has always been and remains a precondition for our future relationship,” he said.
“It was on this basis that we negotiated, concluded and ratified the trade and co-operation agreement on Christmas Eve last year.
“The two agreements are intrinsically linked, one cannot exist without the other.”
However, he ruled out a renegotiation of the protocol.
He said: “Our solutions can become reality if the UK plays its part. That is why we have engaged constructively with the UK in order to agree joint solutions.
“But we also make clear, with the full support of the European Parliament and the member states, that we will not renegotiate the protocol.
“To do so would mean to put at risk the stability in Northern Ireland and it would be unnecessary because solutions are available within the framework of the protocol.”