Video report by ITV News Political Correspondent Libby Wiener
The Prime Minister said Brussels is "not moving in their willingness to compromise" and warned a no-deal Brexit becomes more likely the longer this goes on.
He urged the UK's "European friends to compromise" but said their position is likely to harden the more they believe Westminster can block Brexit.
He said: "There's a terrible kind of collaboration, as it were, going on between people who think they can block Brexit in Parliament and our European friends.
"The more they think there's a chance that Brexit can be blocked in Parliament, the more adamant they are in sticking to their position."
Mr Johnson's remarks, made during a self-styled "People's PMQs" from his Downing Street desk, came after the European Commission insisted Britain needs to explain its ideas on the way forward if talks are to progress.
They also came after former chancellor Philip Hammond accused the Prime Minister of trying to "wreck" the chances of a new Brexit deal, by making demands the EU will not accept.
Mr Hammond said Mr Johnson would commit a betrayal of the referendum if he enacted a no-deal Brexit by listening to the “unelected” saboteurs “who pull the strings” of his Government.
Mr Hammond, who resigned in anticipation of Mr Johnson becoming Prime Minister and who has campaigned vociferously against no-deal, urged the Tory leader to take the UK out of the European Union with a deal in place.
But he said early signs for that “are not encouraging”, warning that demands to abolish the backstop had become a “wrecking” stance over a deal.
"The pivot from demanding changes to the backstop to demanding its total removal is a pivot from a tough negotiating stance to a wrecking one," he said.
The 63-year-old declined to answer questions when approached by ITV News.
“The unelected people who pull the strings of this Government know that this is a demand the EU cannot and will not accede to,” the Tory backbencher wrote in The Times on Wednesday in an apparent swipe at the Prime Minister's top adviser, Dominic Cummings.
Mr Hammond said he was busting two “great myths” over a no-deal Brexit, arguing it will be damaging to the nation – both economically and to the union – and that voters do not back the move.
“Most people in this country want to see us leave in a smooth and orderly fashion that will not disrupt lives, cost jobs or diminish living standards, whether they voted Leave or Remain in 2016,” he wrote.
“Parliament faithfully reflects the view of that majority and it will make its voice heard.
"No-deal would be a betrayal of the 2016 referendum result.
"It must not happen.”
However, Transport Secretary Grant Shapps attacked the former chancellor for not having "prepared properly" for Brexit and said he was "wrong" to have made his recent comments.
He told ITV News: "If you are Philip Hammond you might look at what has happened in the last few years and reflect on whether you have prepared properly."
He added: "I'm afraid to say I think (Mr Hammond) is wrong to say that when what we're now doing is making sure we will leave on October 31, do or die, as the prime minister says.
Mr Hammond also accused “some key figures in the Government” of “absurdly” suggesting no-deal would boost the UK’s economy.
According to The Sun, Mr Hammond and 20 other senior Tories have written to the Prime Minister to say his demands to abolish the backstop “set the bar so high that there is no realistic probability of a deal being done”.
Meanwhile, Speaker John Bercow warned he “will fight with every breath in my body” any attempt by the Prime Minister to suspend Parliament to force through no-deal against MPs’ wishes.
And Work and Pensions Secretary Amber Rudd said she would urge Mr Johnson not to take that controversial move as part of his “do or die” commitment for Brexit by the October 31 deadline.
Mr Bercow told an audience at the Edinburgh Fringe festival that he “strongly” believes the House of Commons “must have its way”, in remarks reported by the Herald newspaper.
“And if there is an attempt to circumvent, to bypass or – God forbid – to close down Parliament, that is anathema to me,” he said.
“I will fight with every breath in my body to stop that happening.”
ITV News Political Correspondent Shehab Khan gives his assessment of the Brexit situation:
Prime Minister Boris Johnson's working majority is just one and 20 of his own MPs speaking out against the government's position is a significant problem.
His Brexit strategy so far has been to ramp up pressure on the EU, demonstrate that the UK is ready and willing to leave with no deal in the hope that in the final moment the EU offers a concession to avoid an outcome that both sides say they don't want.
I've been speaking to senior sources inside Downing Street today and they say they're not very happy with what Hammond's had to say because he's undermined the government's position.
It's demonstrated to the EU that maybe they don't need to offer a final concession because MPs in the Commons might just block a no-deal Brexit.
Kwasi Kwarteng, the business minister, has been criticising Philip Hammond for his intervention.
He said: "(Philip Hammond's) job was to prepare the Treasury and the country to face the eventuality of no deal.
"I remember in the 2017 Budget, he set billions aside to prepare for no deal, he expressly said that, you can look at his speeches.
"Now he's on the backbenches he's actually saying the complete opposite of what he was meant to prepare for."
However, there are many MPs in the Commons who believe they can block a no-deal Brexit and there has been some speculation that Mr Johnson might shut down Parliament to prevent MPs from legislating to stop a no-deal Brexit.
But Speaker John Bercow has reportedly said he will prevent the PM from doing that and MPs will get a say on whether the UK leaves the European Union with no deal.