Negotiating a new Brexit agreement by the crucial EU summit will be "very difficult", Leo Varadkar has warned Boris Johnson ahead of their crunch talks to avert a no-deal exit.

The Prime Minister's chances of a breakthrough with Brussels were looking increasingly unlikely on Tuesday after accusations from Number 10 that the bloc was making it "essentially impossible" for Britain to leave with a deal.

Mr Johnson will hope to gain concessions from his Irish counterpart Mr Varadkar during in-person talks anticipated later this week.

But with the October 31 deadline rapidly closing in, the Taoiseach warned of the challenges of securing a new deal by next week - a key period in the Brexit saga with the summit in Brussels.

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Mr Varadkar said Ireland and the EU would not accept an agreement at "any cost".

"There are some fundamental objectives that haven't changed for the past three years and we need them guaranteed," he told RTE news.

"I think it is going to be very difficult to secure an agreement by next week, quite frankly.

"Essentially what the United Kingdom has done is repudiate the deal that we negotiated in good faith with Prime Minister (Theresa) May's government over two years and sort of put half of that now back on the table and are saying, 'That's a concession'. And of course it isn't really."

The PM had spoken to his Irish counterpart by telephone for about 40 minutes earlier in the day.

Mr Johnson needs a deal sorted by the end of October 17/18 if he is to avoid a dilemma over the Benn Act, which compels him to ask Brussels for an extension if he cannot get an agreement past MPs when he returns, a move he has ruled out taking.

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Earlier there was fury in Brussels following a series of No 10 briefings claiming German Chancellor Angela Merkel had made clear a deal was now "overwhelmingly unlikely".

No 10 sources claimed Mrs Merkel had told the PM that Britain could not leave the EU unless it was prepared to leave Northern Ireland behind in a permanent customs union.

European Council president Donald Tusk accused Mr Johnson of engaging in a "stupid blame game" ahead of next week's crucial EU summit.

"At stake is the future of Europe and the UK as well as the security and interests of our people," he tweeted.

"You don't want a deal, you don't want an extension, you don't want to revoke, quo vadis (where are you going)?"

But Jean-Claude Juncker went on to say that if negotiations fail, "the explanation will be found in the British camp (because) the original sin is found on the islands and not on the continent".

Speaking to the French Les Echos newspaper, the European Commission president added: "A no-deal Brexit would lead to a collapse of the United Kingdom and a weakening of growth on the continent."

The PM also hosted European Parliament president David Sassoli in Downing Street on Tuesday, but the MEP left saying "no progress" had been made.

Mr Sassoli later told the BBC's Newsnight programme: "Angela Merkel's opinions must be taken seriously. We are all very worried because there are only a few days left.

"Because we understand that going out without an agreement leads to having a real problem, if not a real catastrophe."

Mr Johnson had reiterated to the president his warning that the UK would leave by the Halloween deadline regardless of whether a deal was in place.

Hardball tactics from No 10 even alarmed some ministers, after sources warned Britain could break off security co-operation with the EU if it was prevented from leaving on October 31.

Northern Ireland Secretary Julian Smith tweeted that "any threat on withdrawing security co-operation with Ireland is unacceptable".

The dramatic escalation in the war of words between Brussels and London followed a telephone call on Tuesday between Mr Johnson and Mrs Merkel to discuss the latest UK proposal to resolve the deadlock over the Northern Ireland backstop.

EU leaders have dismissed the plan as the basis for a settlement as it would mean the return of customs checks on the island of Ireland, albeit taking place well away from the border between the North and the Republic.

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A No 10 source said Mrs Merkel had told the Prime Minister Ireland must at least have a veto on Northern Ireland leaving the EU with the rest of the UK.

"It was a very useful clarifying moment in all sorts of ways," the unnamed source, quoted by Sky News, said.

"If this represents a new established position, then it means a deal is essentially impossible, not just now but ever."

The PM's official spokesman acknowledged there had been a "frank exchange" with Mrs Merkel and that the talks had reached a "critical point", but refused to be drawn any further on the "source" claims.

The row followed a briefing to The Spectator magazine, also citing a contact in No 10, warning the Government could do "all sorts of things" to get around the Benn Act, which requires the PM to seek a further Brexit delay if he cannot get a deal by October 19.

The source - widely thought to be Mr Johnson's chief adviser Dominic Cummings - said it would treat any support by EU leaders for a new extension as "hostile interference" in UK politics, and that future defence and security co-operation would "inevitably" be affected.

"We won't engage in further talks, we obviously won't given any undertakings about co-operative behaviour, everything to do with 'duty of sincere cooperation' will be in the toilet," the source said.