Boris Johnson and European Commission President Ursula von der Leyen are trying to break the deadlock over a post-Brexit trade deal in Brussels.
The PM is having dinner with the German politician, alongside UK negotiator Lord Frost and the EU’s Michel Barnier, after 30 minutes of initial talks.
Negotiations between the sides are deadlocked amid disputes over fair competition rules and fishing quotas.
Mr Johnson has said the EU has made demands no prime minister could accept.
Before leaving for Brussels, Mr Johnson tweeted that there was “still a good deal to be done” but that the UK would thrive whatever the outcome.
Time is running out to reach a deal before 31 December, when the UK stops following EU trading rules and leaves the 27-member bloc’s internal market and customs union.
Major disagreements remain on access to UK fishing waters, how far the UK will diverge from EU environmental and labour standards and how a deal will be policed.
Mr Johnson and Ms von der Leyen, who is representing the leaders of the 27 EU nations, paused for photos as she welcomed him to the Commission’s headquarters.
After removing their masks for a matter of seconds, the PM was encouraged to re-attach his own rather than put it in his pocket, telling his host “you run a tight ship here, Ursula, and quite right too”.
The two leaders are currently holding a working dinner, during which they will talk through a list of the major sticking points with their negotiators, Lord Frost and Mr Barnier, and a handful of officials.
The menu consisted of a choice of pumpkin soup or scallops for starters followed by a main course of steamed turbot, mashed potato with wasabi and vegetables. Dessert is pavlova with exotic fruit and coconut sorbet.
The hope is that the meeting will open up the political space for the negotiators to resume their work in the coming days.
It comes at a critical time in the process, with EU leaders holding their last scheduled summit of the year in Brussels on Thursday and Friday.
Charles Michel, the head of the European Council, has said it is unlikely that the 27 leaders will formally discuss the trade negotiations but Ms Von der Leyen will brief Emmanuel Macron, Angela Merkel and others.
Ahead of Wednesday’s dinner, it emerged the European Commission is set to publish its contingency plans for a no-deal outcome on Thursday morning.
A senior EU diplomat said it was “impossible to know” what might result from the leaders’ meeting and it was up to the UK decide whether it wants a deal.
“The solutions sought by the commission and the negotiator take into account the British narrative,” he said.
“We can have a philosophical discussion about what sovereignty is but the British narrative is taken into account in a constructive and respectful way.”
Speaking in Parliament earlier on Wednesday, Mr Johnson pinpointed the areas where he believed the EU needed to give ground in order to seal a deal.
“Our friends in the EU are currently insisting that if they pass a new law in the future with which we in this country do not comply or don’t follow suit, then they want the automatic right to punish us and to retaliate.
“Secondly, they are saying that the UK should be the only country in the world not to have sovereign control over its fishing waters. I don’t believe that those are terms that any prime minister of this country should accept.”
BBC