London (CNN) Relations between the European Union and the British government soured badly on Tuesday after Downing Street indicated that Brexit talks were on the verge of collapse and blamed German chancellor Angela Merkel for their failure.

European Council President Donald Tusk responded by claiming that Prime Minister Boris Johnson had no intention of concluding a Brexit deal, and accused him of playing a "stupid blame game."

Irish Prime Minister Leo Varadkar also cast doubt on a Brexit breakthrough, telling national broadcaster RTE it would be "very difficult" to secure an agreement by next week, following a phone call with Johnson earlier Tuesday.

The bad-tempered exchanges indicated that relations between the two sides have become deeply strained, with the deadline for the UK's departure from the European Union looming and no deal yet agreed.

The bitterness appears to have flowed from a telephone call between Johnson and Merkel in which the two sides failed to agree on the thorny issue of the post-Brexit status of Northern Ireland, a fraught question that has dogged the talks.

An official UK government spokesperson admitted there had been a "full and frank exchange of views" on the call with Merkel -- diplomatic code for an argument.

According to a different senior government source, Johnson laid blame on the EU for a failure to engage with new proposals he presented to the EU last week. According to the source, Johnson also claimed that "some" European officials are "clearly hoping a second referendum will reverse Brexit," but assured Merkel that this "will not happen."

The source said Downing Street was downbeat about the potential for a deal. "Talks in Brussels are close to breaking down despite the fact that the UK had moved a long way," the source said.

.@BorisJohnson, what's at stake is not winning some stupid blame game. At stake is the future of Europe and the UK as well as the security and interests of our people. You don't want a deal, you don't want an extension, you don't want to revoke, quo vadis? — Donald Tusk (@eucopresident) October 8, 2019

After similar briefings appeared in the UK media on Tuesday, Tusk responded harshly. "What's at stake is not winning some stupid blame game," Tusk posted on Twitter in a comment aimed directly at Johnson. "At stake is the future of Europe and the UK as well as the security and interests of our people. You don't want a deal, you don't want an extension, you don't want to revoke, quo vadis [where are you going]?"

Germany pointedly refused to comment on the call with Merkel. "As is customary, we don't report from such confidential conversations," a German government spokesman said.

Even as Downing Street expressed pessimism about the outcome of talks, British and EU negotiators were meeting in Brussels for technical discussions Tuesday. "These talks are reaching a critical point," the UK government spokesman said. "The UK has moved a long way, and now we need to see movement from the EU side."

A separate phone call between Johnson and his Irish counterpart on Tuesday also appeared to do little to ease concerns, with Varadkar later telling RTE: "Essentially what the UK has done is repudiated the deal that we negotiated in good faith with Prime Minister May's government over two years and have sort of put half of that now back on the table and saying that's a concession.

"Of course it isn't."

The Irish and British prime ministers are due to meet in person later this week.

With just weeks until the October 31 deadline for the UK's exit from the EU, European Parliament President, David Sassoli, warned of a "catastrophe" if no deal is reached in time.

"Angela Merkel's opinions must be taken seriously," Sassoli told BBC Newsnight after meeting with Johnson at Downing Street on Tuesday.

"We are all very worried because there are only a few days left," he said. "Because we understand that going out without an agreement leads to having a real problem, if not a real catastrophe."

The next summit of EU leaders is on October 17 and 18 and time is running out for both parties to negotiate a new deal by the latest Brexit deadline of October 31.

If the PM doesn't get a deal by October 19, he is obliged by law to seek a new extension to the Brexit process. But Johnson has long maintained that he would take the UK out of the European Union on October 31 "do or die."