Downing Street has said the government will not back away from its demand to kick off negotiations on a post-Brexit trade deal as soon as possible – even though the European commission president, Jean-Claude Juncker, flatly dismissed the idea on Tuesday.

As the third round of Brexit talks resumes in Brussels, Juncker said: “We need to be crystal clear that we will commence no negotiations on the new relationship – particularly a new economic and trade relationship – between the UK and the EU before all these questions are resolved.”

The EU27 have consistently said they will require sufficient progress to be made on three issues – the Northern Ireland border, the divorce bill, and the future status of EU citizens – before negotiations can move onto the future partnership between Britain and the EU.

But earlier this month, the Brexit secretary, David Davis, reopened the question of the phasing of the talks, which he had previously described as “the row of the summer”.

Asked about Juncker’s remarks on Tuesday, the prime minister’s deputy official spokeswoman said: “Our desire is to discuss both at the same time: we’ve repeatedly said that, and that’s what we’re working towards.”

She added: “We have just begun the third round today; we felt the first two rounds were positive and constructive, and as you’ve seen over the summer we’ve published numerous position papers, as well as future partnership papers. We’ll see where we get to on Thursday, but we believe we’re in a good position, and would like to move on to discuss our future relationship.”

Davis has said it is impossible to resolve questions such as the Northern Ireland border without an idea of what future trading relationship Britain will have with the EU. The published papers included proposals on a future customs deal, and on how legal disputes could be resolved without the direct intervention of the European court of justice.

However, the commission appears to have been irked by this approach – particularly since none of the papers tackled the thorny question of what financial contribution Britain believes it will be liable to make when it leaves.

Talking about the papers, Juncker said: “None of those is actually satisfactory. So there is still an enormous amount of issues which remain to be settled.”

But the Downing Street spokeswoman said: “We believe the EU needs to show more imagination and flexibility when it comes to these discussions.”

This week’s talks, which are due to continue until Thursday, are expected to be technical, and both sides have played down the likelihood that there will be any tangible outcome.

The government is hoping the next round of talks, in September, will achieve sufficient progress to convince EU27 leaders to signal at the European council in October that talks can move on.

The spokeswoman said: “There are lots of issues there where we believe you can’t separate withdrawal from future relationship, and that’s what we’re seeking to agree by October council – that we can move on to talk about our future relationship.”