In a joint statement, Johnson and von der Leyen claimed it was “responsible at this point to go the extra mile”.
The unexpected statement was issued after the two leaders held a phone call in which they discussed “major unresolved topics”.
Johnson and von der Leyen have reportedly instructed their negotiators in Brussels to continue talking “to see whether an agreement can even at this late stage be reached”.
UK and EU negotiators must agree a deal – and have it ratified by their respective parliaments – by December 31.
But the PM has tried to dampen down expectations of a quick breakthrough by once again saying that a “no deal scenario” was “most likely”.