The British prime minister wants a deal by October 15th, when the leaders of the 27 EU countries meet in Brussels.
Negotiators are meeting in the Belgian capital for three days of talks ahead of Thursday’s European Council summit.
Following reports that the deadline could slip, Downing Street insisted that Mr Johnson remained committed to the October 15th date and pointed out that the EU’s Michel Barnier had said the “moment of truth” in the negotiations would come in the middle of this month.
In recent days Mr Johnson has spoken to German chancellor Angela Merkel and French president Emmanuel Macron, but gaps still remain between the UK and EU sides over fishing rights and the so-called “level playing field” on state subsidies, workers’ rights and environmental standards.
The British prime minister’s negotiator Lord Frost and his counterpart Mr Barnier were meeting for talks in Brussels after discussions last week in London.
Mr Johnson’s official spokesman said: “David Frost and the UK negotiating team are in Brussels today for further talks as part of the intensified process that was agreed by the PM and (European Commission president) Ursula von der Leyen.
“These talks will continue until Wednesday. Then the European Council takes place at the end of this week.
“We will work as hard as we can to see if we can get an agreement by October 15.
“The EU themselves indicated to the UK negotiating team in July that mid-October was the last possible date for a deal.”
The spokesman said the UK was “committed to working hard this week to seek to bridge the gaps that remain, in particular on fisheries and the level playing field”.
Downing Street repeated its insistence that it would be prepared to walk away without a comprehensive deal and conduct business with the EU in the same way as Australia, a country on the other side of the world which has nothing like the same volume of trade with the bloc.
“The PM has been very clear in his conversations with European leaders that time is in short supply and that while we would like a deal and are committed to work hard to get one, if necessary then we will be prepared to move to trading with the EU on Australian-style terms,” the spokesman said.
The European Commission said talks were continuing but played down speculation they were now in what has been dubbed the “tunnel” or “submarine” – the final stages of negotiations conducted in the utmost secrecy with no leaks.
Commission spokesman Eric Mamer said: “As far as I know they’re not meeting either in a tunnel or a submarine but in offices and therefore it’s a completely normal schedule and format of negotiations.
“Of course negotiations have been intensified over the past weeks as Prime Minister Johnson and President von der Leyen agreed during their phone call two weeks ago and therefore we are in an intense phase of negotiations.”