Brexit talks are going "well" but the EU needs to show flexibility, Cabinet Office Minister Michael Gove has said.
He said there is a "big philosophical difference" between the sides, and the EU wants the UK "to follow their rules even after we have left the club".
The EU's Michel Barnier has suggested the UK's demands are "not realistic" and warned of a looming stalemate.
The UK said "very little progress" had been made after the latest post-Brexit trade talks concluded on Friday.
The two sides have been discussing their future economic and security partnership following the UK's withdrawal from the 27-member bloc on 31 January.
The UK has said it will not extend the negotiation process beyond 31 December, despite calls for the government to allow more time for a deal to be reached due to the coronavirus pandemic.
One of the sticking points during negotiations has been access to fishing waters. Speaking to the Andrew Marr programme, Mr Gove said "they [the EU] want to have the same access to our fish as they had when we were in the EU".
He challenged the EU to show "a little bit of their fabled flexibility", earlier telling Sky News that he was "confident a deal could be done".
On Friday, Mr Barnier - the EU's chief Brexit negotiator - said the UK could "not have the best of both worlds" adding he was "still determined but not optimistic" about the chances of reaching an agreement.
He also said the EU would not accept a deal "at any price" and was stepping up preparations for a no-deal outcome, in which the two sides would trade with each other under World Trade Organization rules.
Insisting the EU would not negotiate "in haste", Mr Barnier said the UK must consider whether it was possible to agree a deal before the end of the year, when the current 11-month transition period is due to end.
During the transition period the UK continues to follow EU rules - and the government has insisted it does not want to extend this period.
Speaking to Sky News, shadow cabinet office minister Rachel Reeves said Labour "absolutely do not want" the UK to end the transition period in December without a deal and urged the government not to "rush this".
"The last thing our country and our economy needs at the moment is a further shock that could put jobs and livelihoods at risk," she said.
Meanwhile MPs from the other opposition parties, including the SNP, Lib Dems and the Green Party, have written to Mr Barnier expressing their support for an extension to the transition period.
The letter said there was "significant opposition to the UK government's extreme position", adding that an extension would "enable these detailed and defining negotiations to be conducted at a time when, we hope, the efforts of national governments and the European Union will not be engaged solely with dealing with the dreadful Covid-19 epidemic".