The Foreign Secretary and European vice-president to meet again on January 24 following talks at Chevening.
However she refused to rule out the possibility the UK could invoke Article 16 – suspending part of the arrangements in the protocol – if they could not agree a way forward.
“We have had constructive talks with the EU. We are now going to going into intensive negotiations to work towards a negotiated solution to sort out these very real issues for the people of Northern Ireland,” she said in a pooled broadcast clip.
“I think there is a deal to be done. I do want to make progress. Clearly if we don’t make sufficient progress we will have to look at the alternatives, but my absolute desire is to get a deal that works for the people of Northern Ireland.”
Ms Truss assumed responsibility for the negotiations with the EU following the resignation of the Brexit minister Lord Frost last month.
The Government is seeking substantial changes to the protocol – which forms part of the Brexit Withdrawal Agreement – arguing that it is hampering the free movement of goods between Northern Ireland and the rest of the UK and damaging community relations.
In a joint statement, Ms Truss and Mr Sefcovic said: “The meeting took place in a cordial atmosphere. They agreed that officials would meet next week in intensified talks and that the principals would meet again on January 24.
“We share a desire for a positive relationship between the EU and the UK underpinned by our shared belief in freedom and democracy.”