The Brexit secretary, David Davis, and the EU’s chief negotiator, Michel Barnier, have clashed over the UK’s exit bill and Britain’s request for a transition period after Theresa May’s speech in Florence last week failed to unlock the stalemate in negotiations.

On the first day of the fourth round of talks, Barnier said the prime minister’s €20bn (£17.6bn) offer did not mean the UK would be given a transition period or that negotiations could move on to the detail of a future trading relationship.

“It remains more necessary than ever to create the trust that we need to set up and build upon our future relationship,” he said, adding that it was up to Britain to provide clarity with time running out before it leaves.

During a joint appearance in Brussels, Davis insisted there “could be no excuses for standing in the way” of progress this week and it was “obvious” that discussions on the financial settlement needed to be had in the context of talks over the future relationship.

Barnier’s opening remarks are likely to disappoint No 10 and infuriate senior Brexit supporters in the government who believe May’s Florence speech was a generous offer to the EU.

Boris Johnson, the foreign secretary, said during a visit to the Czech Republic that the “ball is in the [EU’s] court” after May promised to carry on paying into the EU until at least 2020 and offered to enshrine the rights of EU citizens living in the UK in the Brexit withdrawal treaty.

“We are offering a great deal on citizens, a great deal on money and an unconditional commitment to the defence of Europe. Let’s hope we can move this thing forward and get these negotiations going,” Johnson said in Prague.

He then headed to Romania and Slovakia as part of “mission to explain the Florence speech and what it means for our determination to get on with negotiations over Brexit”, while May placed an opinion article in a Czech newspaper, as the UK continued its efforts to bypass the European commission and take its arguments straight to member states.

However, EU member states have made clear that authority over the talks lies with Barnier, who insists Brussels needs to see “sufficient progress” on citizens’ rights, the financial settlement and the Irish border before it will discuss future trade.

Coming out of a meeting with EU ministers from the 27 other member states, Barnier suggested little had changed in the state of the discussions.

“A discussion that is going to take place because the UK is asking for it on this transitional period does not mean we will no longer need to achieve sufficient progress,” he said.

“We are not going to mix up discussions on debts and discussion on the past commitments. We are not going to mix up those subjects, which are part of an orderly withdrawal, on a discussion of our future relationship.”

Davis said he still expected this week’s round of talks to build on May’s speech, saying the UK was “absolutely committed to working through the detail”.

“We are laying out concrete proposals and there are no excuses for standing in the way of progress … It will take pragmatism from both sides to make headway and I hope we can achieve that this week.”

But Barnier offered little succour to the UK’s cause and directly contradicted Davis’s claims over the weekend that Britain would no longer be under EU law in 2019, should it seek a transition period.

“The EU has to decide whether to have a transitional period and whether it is in its interest. Any transition has to respect the regulatory and financial framework of the single market,” he said.

“As we said, we are talking about prolonging and extending EU legislation for a certain amount of time. That would mean we would have to continue with [such] things as the budget, supervision, judicial control and controls of EU rules and regulations. So that would have to continue to apply.”

May has accepted that the UK would have to abide by existing EU rules during the transition period but there are divisions within the cabinet over whether Britain should have to submit to new ones made during the two-year timeframe.

Johnson has been fighting against submission to new rules and in favour of the minimum possible transition period and for the UK to make a clean break with the EU after 2021.

But this has created divisions with Philip Hammond, the chancellor, who is in favour of a transition preserving the status quo, avoiding a “no-deal Brexit” at all costs and staying as close as possible to the single market after 2021.

No 10 hoped May’s Florence speech would draw a line under her Brexit difficulties and allow her to focus on domestic policy during the Conservative party conference next week, but infighting within her cabinet and speculation over her leadership are likely to overshadow the event.

At Labour’s conference, Keir Starmer, the shadow Brexit secretary, accused May of “robotically marching towards an extreme Brexit, focused on her own survival not the national interest”. He said his party would consider a “new single-market relationship” with the EU.

“Whether you’re in the front seat with Theresa May, or in the backseat with Boris Johnson, there’s nothing patriotic about joy-riding our country’s economy off a cliff,” Starmer said.

Johnson’s actions over the past few weeks, including writing a 4,000-word personal blueprint for leaving the EU, published in the Telegraph, has been seen as a sign he is trying to goad May into sacking him over Brexit.

Further tensions erupted over the weekend when Johnson’s allies claimed he was responsible for steering May away from a Norway-style soft Brexit in her Florence speech on Friday and for seeing off Hammond’s demands for a longer transition.

Johnson’s attempt to cast himself as the saviour of a proper Brexit has been dismissed by Davis, while Hammond said on Monday he “was entirely in accord” with May’s proposal for a transition period of about two years.

Additional reporting Jennifer Rankin in Brussels