EU leaders have told Boris Johnson there is no way to strike a Brexit agreement before this week’s summit, destroying his hopes of presenting a deal to parliament at a special sitting on Saturday.

Finland’s Prime Minister Antti Rinne, whose government currently holds the rotating EU presidency, warned there was no “practical or legal way” to find an agreement before Thursday’s meeting of EU leaders in Brussels – while Spain’s foreign minister said “more time” could be needed.

Simon Coveney, the Irish deputy prime minister, also suggested on Monday that talks might have to “move into next week” though he said it was “too early to say”.

Speaking in Helsinki alongside Belgian prime minister Charles Michel, who is the next European Council president, Mr Rinnie told reporters: “I think there is no time in a practical or legal way to find an agreement before the EU Council meeting. We need more time.”

Spanish foreign minister Josep Borrell, who is set to take over as the EU’s foreign affairs chief, meanwhile told reporters outside a meeting in Luxembourg that there might be a need to “stop the watch” and ask for more time.

“You know, in Europe, we always take decisions on the edge of the precipice, on the edge of the cliff,” he said. “Even when the last minute comes, then we stop the watch and say that we need technically more time to fulfil all the requirements, all the last minute requirements.”

There was little progress to show from technical talks in Brussels, despite discussions continuing over the weekend and both sides labelling negotiations as “constructive”. A negotiating “tunnel” covering the talks means that there is little official information about what is being discussed in the room between the two sides.

The two sides are understood to be working on a legal text covering customs arrangements for the Irish border – with the need for more time potentially down to the painstaking legal nature of the work as much as disagreement in principle. The EU insists that any proposals must be “legally operable” before being signed, meaning the plans must be a complete watertight legal text.

A delay to talks beyond this week’s gathering of EU leaders would complicate matters as under UK law the prime minister will have to request an extension to Article 50. The Commons is expected to hold an unprecedented emergency weekend sitting on Saturday to assess progress.

Delays could also mean that further emergency summit may be required to sign off a deal, if one were reached – as it was in November when Theresa May got her last minute agreement.

Boris Johnson has publicly said he will not seek an extension, though the government told a UK court that that it would comply with the so-called Benn Act, which requires the prime minister to ask for a further delay to avert a no-deal exist on 31 October.

“I think it’s too early to say, even though we’re only a few days away from the summit. It’s too early to say whether it’s possible to get a breakthrough this week or whether it will move into next week,” Mr Coveney, the Tánaiste, told Irish broadcaster RTÉ at a ministerial meeting in Luxembourg.

“What they’re attempting to do here is to write a legal text for an international treaty, that is a Withdrawal Agreement. That means it’s got to be watertight, it’s got to stand up to full scrutiny and legal challenge potentially, and what they’re trying to do is complicated.

“They’re trying to put in place an arrangement that is NI-specific, that protects UK interests and EU interests, in a way that’s quite complex. So we need to give negotiating teams space to do that, I think there is good will and a political determination to get this done.

“It is being left very late in the day but we shouldn’t write off this summit as a potential opportunity for agreement.”

Charles Michel and Finnish prime minister Antti Rinne hold a joint press conference in Helsinki on Monday (EPA)

Downing Street again on Monday ruled out any delay. The PM’s official spokesman told a Westminster briefing: “The talks remain constructive but there is still a lot of work still to do.”

Asked whether the PM was sticking to his 31 October pledge, the spokesman said: “I think the prime minister has always said we need to leave the EU on the 31.

“We need to leave the EU on 31 October to restore trust in our democracy. That is what the prime minister is committed to achieving.”

The spokesman said it was “news to me” that a technical extension could be possible.

Asked if this was the last chance to get a deal, he said: “The PM has set out we are under great time pressure and has repeatedly stressed the importance of us completing this process so we can leave on 31 October.”

The spokesman added: “If after three years of debate we are able to secure a deal that parliament can support, the public would expect parliament to work around the clock to pass that legislation in order to allow us to leave on that date.”

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There is also uncertainty back in Westminster as to whether a deal could even pass the House of Commons. The DUP signalled again at the end of last week that it would not back any plan that treated Northern Ireland differently in customs terms to the rest of the UK – though to be the only way to solve the border deadlock.