The EU has said it is willing to "intensify" talks on a trade deal with the UK this week to try to break the impasse between the two sides.
Its negotiator Michel Barnier said the bloc was prepared to discuss all areas of disagreement, including fishing and competition, based on legal texts.
Michael Gove said he welcomed the bloc's latest "constructive" step.
Later, No 10 said there was "no basis to resume talks" unless there was a "fundamental change" from the EU.
The UK has accused the EU of dragging its feet and failing to respect its sovereignty in the negotiations.
In a Commons statement, Cabinet Office Minister Mr Gove said his "door was not closed" to further talks but the EU needed to change its position for the process to continue.
After a call between Mr Barnier and the UK's chief negotiator, Lord Frost, Downing Street released a statement saying the EU needed to try to find an agreement "between sovereign equals".
On Friday, No 10 suggested formal negotiations were "over" as the EU was not serious about discussing the details of a free trade agreement similar to the one it has with Canada - the UK's preferred outcome.
Prime Minister Boris Johnson said the UK should "get ready" to trade with the EU from 1 January, when it leaves the single market and customs union, without a specific agreement.
But following a video call with his UK counterpart Lord Frost on Monday, Mr Barnier said he was willing to accelerate the process in the coming days to try to bridge the gap between the two sides.
🇪🇺🇬🇧 I just spoke to @DavidGHFrost.— Michel Barnier (@MichelBarnier) October 19, 2020
As stated by President @vonderleyen on Friday, I confirmed that the EU remains available to intensify talks in London this week, on all subjects, and based on legal texts.
We now wait for the UK’s reaction.
Mr Barnier suggested all subjects would be on the table and the discussions would be based on specific legal texts, which the UK has accused the EU of refusing to consider in recent weeks.
In response, Lord Frost tweeted that the proposal to intensify work had been noted, and added: "But the EU still needs to make a fundamental change in approach to the talks and make clear it has done so."
Constructive discussion with @MichelBarnier today. Noted his proposal to intensify work, as we have been asking. But the EU still needs to make a fundamental change in approach to the talks and make clear it has done so. We will stay in close touch.— David Frost (@DavidGHFrost) October 19, 2020
Updating MPs on the state of the talks, Mr Gove said the EU's latest move was a positive one and suggested the UK would respond in kind.
He said: "Even while I have been at the despatch box, it has been reported that there has been a constructive move on the part of the EU and I welcome that.
"We need to make sure we work on the basis of the intensification they propose and I prefer to look forward in optimism rather than look back in anger."
He added: "If there has been movement, and there seems to be movement, then no-one would welcome it more than me but what we can't have from the EU is the illusion of engagement without the reality of compromise."
Some senior Conservatives have urged the government to walk away from the talks, suggesting the EU is no longer negotiating in "good faith".
Former Tory leader Iain Duncan Smith said the EU's "refusal" to engage in meaningful talks on trade in financial services and agricultural products was a breach of the terms of the withdrawal agreement governing the UK's exit.
The government has said the UK will prosper whatever the outcome of the negotiations, as it will be able to exercise freedoms not available while being an EU member.
But business groups have warned the UK's fallback option of a so-called "Australian-style" arrangement - where UK-EU trade will default to World Trade Organization rules - would be disastrous as it would see tariffs on goods moving across the channel.
With less than 75 days to go before the transition period ends on 31 December, the government has urged business to step up its preparations for the looming changes to trading rules.
The PM will hold a meeting with industry groups on Tuesday to emphasise the need for action.
Labour has said the government only has itself to blame for the current uncertainty, shadow Cabinet Office minister Rachel Reeves calling on ministers to be "honest" about the effect on the UK of not agreeing a trade deal.
And former Conservative Prime Minister Theresa May suggested the implications of failing to agree a future partnership would also be highly damaging for the UK's security.
Mrs May, who quit last year after Parliament rejected her withdrawal agreement three times, said the UK "should not be resigned" to the prospect of failing to agree a deal over law enforcement and information sharing.
She warned that "if the UK walks away with no deal, then our police and law enforcement agencies will no longer have the necessary access to databases in order to be able to continue to identify and catch criminals and potential terrorists in order to keep us safe".
In response, Mr Gove said "significant progress" had been made in terms of security co-operation but the EU could not make access to databases conditional on the UK accepting the jurisdiction of the European Court of Justice.