Boris Johnson has been clear with the EU that the time left to get a post-Brexit trade deal in place is in "short supply", Downing Street says.
The prime minister has set a deadline of this Thursday, after which he has said the UK is ready to "walk away".
No 10 said the time limit was still in place and the government was trying to "bridge" disagreements over fishing rights and state aid for businesses.
Meanwhile, the UK's negotiating team is in Brussels for further talks.
These come after Mr Johnson and European Commission President Ursula von der Leyen called for an intensification of discussions.
The prime minister set his deadline to coincide with the start of an EU summit, at which leaders will discuss the state of the trade talks.
Both sides have spoken of progress in the last couple of weeks, but there are still major disagreements on two issues in particular.
First, the EU wants the UK to follow its rules on state aid - financial assistance given by government to businesses - but the UK says it would undermine independence.
Second, the UK wants full access to EU markets to sell its fish, but in return the EU is demanding full access for its fishing fleets to UK waters - which the UK does not want to provide.
It has been reported that France is ready to rule out a deal if the UK does not back down over fishing rights.
If no agreement is reached, the UK and EU would do business under World Trade Organisation rules from 1 January next year, which would mean tariffs on goods.
Last week, Irish Prime Minister Micheál Martin said "movement" was required before "end-state negotiations" could begin.
The UK's chief negotiator, Lord Frost, said he would advise the prime minister on whether the UK's set conditions for a deal have been met following his talks with EU counterpart Michel Barnier in Brussels.