The intensive diplomacy comes with seemingly just days to go for an agreement on a future trade settlement to be struck between Britain and Brussels.
Mr Johnson told the German leader a deal was the desirable outcome, but he was prepared to leave the Brexit transition period at the end of the year on Australian-style terms with the EU if necessary.
Both sides have said an agreement needs to be struck in October to ensure sufficient time for ratification.
Mr Johnson has previously said he wants agreement on a free-trade deal by the time of next week’s EU summit in the Belgian capital on Thursday.
Referring to the Prime Minister, a Downing Street spokesperson said: “He outlined the current situation with respect to negotiations on the future relationship between the UK and the EU, emphasising the UK’s desire to reach an agreement.
“The Prime Minister stressed that, while achieving a deal in the coming days would be beneficial for both sides, the UK was also prepared to end the transition period on Australia-style terms if a deal was not possible.
“The Prime Minister emphasised that progress must be made in the coming days to bridge the significant gaps, in particular in the areas of fisheries and the level playing field, through the process of intensive talks between chief negotiators.
The telephone talks came ahead of UK and EU negotiators resuming informal negotiations next week in Brussels, with time running out for agreement on a post-Brexit trade deal.
Lead negotiators Michel Barnier and Lord Frost met on Friday for face-to-face discussions in London.
The Prime Minister and Mrs Merkel also discussed the coronavirus crisis in their bilateral discussions.