The prime minister struck a downbeat tone before meetings with the leaders of Germany, France, the Netherlands and Ireland – with little more than three weeks to his own final deadline for an agreement.
Mr Johnson also dismissed the idea that Angela Merkel and Emmanuel Macron would be more flexible than the European Commission, which comprehensively rejected his alternative to the Irish backstop last week.
“This is not going to be the moment,” he told reporters before arriving in the US. “I don’t wish to elevate excessively the belief that there will be a New York breakthrough.”
Mr Johnson continued to insist a “great deal of progress has been made” – a belief ridiculed in Brussels and other EU capitals – but added: “However, there are clearly still gaps, still difficulties.”
In the past, No 10 has held out the hope that Ms Merkel, in particular, would apply pressure to ease the rigid mandate being pursued by the Commission.
But, asked if that was his hope, the prime minister shrugged and said: “We, in the UK government, respect the primacy of the European Commission when it comes to these negotiations.
“In the end, we understand that, if we can do a deal, it must be done through Michel Barnier and Jean-Claude Juncker.”
Last Friday, a leaked memo from the Commission to EU diplomats laid bare the gulf between the two sides, ahead of a crucial summit on 17 October – itself only two weeks before the UK’s scheduled departure date.
It said the latest British proposals did not provide “legally operational solutions” and would lead to a regulatory and customs border in Ireland.
EU sources also said that Britain had “gone backwards” on proposals from the prime minister for an all-Ireland agrifood zone, to avoid the need for border checks after Brexit.
And Mr Barnier complained that three informal negotiating papers sent to Brussels provided less detail on the government's plans than previously set out by David Frost, the prime minister's chief negotiator.
A paper covering food safety and animal and plant health had “no clarity”. The other documents concerned proposals on customs and manufactured goods.
Mr Johnson also continued to insist it was “absolute nonsense” that his five-week shutdown of parliament was to avoid scrutiny of the Brexit crisis by MPs.
He argued that parliament “has been sitting for the longest period since the Civil War” and that it was “100 years” since it sat at the end of September, or in early October, when party conferences are held.
“We must have a Queen’s Speech, we have a big domestic agenda and we have to get on with tackling the priorities of the British people,” the prime minister said – adding it was “absurd to be totally fixated on Brexit”.