Michel Barnier had tried to assuage some of the prime minister's concerns about the state of negotiations in a telephone conversation with his counterpart Lord Frost on Monday afternoon.
The EU's chief negotiator had said the EU would be happy to hold talks on "all subjects, and based on legal texts" – a demand Mr Johnson had made as a condition for restarting negotiations.
But despite Cabinet minister Michael Gove branding the intervention a "constructive move", Downing Street was less up-beat, warning that "the UK continues to believe there is no basis to resume talks".
Mr Barnier had wanted to come to London on Monday to hold discussions, and promised to work through the weekend, but No.10 had told him to stay away and said there would be "no point".
Speaking in the Commons immediately after the phonecall, Michael Gove, the cabinet office minister, 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 European Union and I welcome that, and obviously we need to make sure that we work on the basis of the proposed intensification that they propose.
The cabinet minister added: "It is the case that my colleague David Frost was in conversation with Michel Barnier. I now believe it is the case both that Michel Barnier has agreed both to the intensification of talks but also to working on legal texts.
"I think a reflection of the strength and resolution that our prime minister showed in stark contrast to the approach that the opposition has often enjoined us of simply accepting what the EU want at every stage."
But shortly after Mr Gove's comments, a Downing Street spokesperson struck a different tone, telling reporters: "The UK has noted the EU’s proposal to genuinely intensify talks, which is what would be expected at this stage in a negotiation.
"However, the UK continues to believe there is no basis to resume talks unless there is a fundamental change of approach from the EU.
"This means an EU approach consistent with trying to find an agreement between sovereign equals and with acceptance that movement needs to come from the EU side as well as the UK. The two teams agreed to remain in close touch.”
The UK side was angered by EU leaders last week, who used a Brussels summit as a platform to warn that any further progress in talks would have to be based on concessions by the UK.
The incident was embarrassing for Boris Johnson, who had stretched a previous deadline until the end of the summit to wait for the leaders' intervention.
Labour MP Hilary Benn, who chairs parliaments' EU negotiations committee, called for talks to resume as quickly as possible.
"Despite what the secretary of state said in his opening remarks it's quite clear talks are continuing and I think the war of words now need to stop," he told the Commons on Monday.
"Both sides need to get together and agree a deal recognising that both have to compromise."
Brexit trade talks have been at an impasse over issues including fishing access and state aid rules.
If no trade deal is agreed with the EU and implemented before the end of the year, the UK will leave the single market and customs union and begin to trade on World Trade Organisation (WTO) terms.
UK businesses would have to pay high tariffs on goods and abide by restrictive quotas. Economics this it would cause serious economic disruption in both the short and long term. The arrangement is a default state of affairs and does not require the agreement of either side.
Earlier on Monday the government admitted that the "Australia-style" Brexit deal trumpeted by ministers is effectively a no-deal.
Cabinet minister Alok Sharma was unable to explain the difference between the two terms, and when pressed admitted it only came down to "semantics".
"You can use the phrase 'no-deal' but the point is that it is a deal," he told LBC radio. "It's a question of semantics at the end of the day, sure."
Asked whether the government should stop using the term "Australia-style deal" because it would mislead the public, the business secretary said:
"I don't think we should stop saying Australia. People will understand quite clearly what that means. You can either go down a WTO route, otherwise you can go down the route of Canada which is what I want to get to."