A Foreign Office source told The Telegraph that Ms Truss wanted urgent progress on tailor-made trade rules for Northern Ireland.
They said: “Liz invited Sefcovic at the earliest opportunity and wants to move forward with the talks.
“She wants urgent progress. She is committed to getting things done and finding a fair, proportionate and lasting solution that genuinely resolves the issues and protects the Good Friday Agreement. “
Discussions are expected to continue until January 14, with the summit seen as an attempt to end the feud over the protocol and restore UK-EU relations.
Ms Truss is expected to warn Mr Sefcovic that triggering Article 16 temporarily suspending parts of the protocol remains an option.
The UK argues that under current arrangements EU border controls on UK goods have a chilling effect on trade to Northern Ireland.
The foreign minister’s allies also stress that she will demand “urgent progress” in talks to prevent a hard border on the island of Ireland.
Ms Truss was appointed to oversee Brexit negotiations with the EU last month following the resignation of Lord Frost, who voiced concerns about the “leadership” of Boris Johnson’s government.
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However, if the negotiations are unproductive, the government could suspend Article 16 – thus ending Ireland’s maritime trade border from the EU’s point of view.