SALZBURG, Austria 20 Sep - Theresa May's proposed new economic partnership with the EU "will not work", the head of the European Council has said.
Mr Donald Tusk said the plans risked undermining the EU's single market.
He was speaking at the end of an EU summit in Salzburg where leaders of the 27 remaining member states discussed Brexit.
UK prime minister Theresa May said her proposals were the "only serious credible" way to avoid a hard border in the Northern Ireland.
Responding to Mr Tusk's remarks, she said there was "a lot of hard work to be done" to reach an agreement but added that the UK was preparing for no-deal.
The UK is due to leave the EU on 29 March 2019, and both sides are trying to reach a deal in time.
There is still no agreement on issues including how to avoid new checks on the Northern Ireland-Republic of Ireland border.
At a press conference, Mr Tusk said there were some "positive elements" in the UK's blueprint for future relations with the EU, which was agreed by ministers at Chequers in July.
But, he added: "The suggested framework for economic cooperation will not work."
Mr Tusk added that October would be the "moment of truth" for reaching a deal, and that "if the conditions are there" an additional summit would be held in November to "formalise" it.
There is still no agreement on issues including how to avoid new checks on the Northern Irish border.
At the EU summit on Wednesday evening Mrs May stressed her "serious" proposals for future co-operation would ensure a "shared closed relationship".
European Commission chief Jean-Claude Juncker described her 10-minute presentation as "interesting".
"It was polite, it was not aggressive, she was doing her job," he told reporters as he arrived for a second day of talks.
Speaking to BBC Radio 4's Today programme, two of the EU leaders said they hoped the UK would hold another referendum on Brexit, in the hope of reversing the 2016 result.
Maltese Prime Minister Joseph Muscat said most of his counterparts would like the "almost impossible" to happen.
Andrej Babis, the Czech Republic's prime minister, added he hoped the British people might change their minds.
But Mrs May said there was no question of the UK seeking to extend its EU membership.
The UK is due to leave the EU on 29 March 2019, and both sides are trying to reach a deal in time, with a crunch summit specially convened in mid-November.
Before the leaders gathered for the second day of the summit, Mrs May held talks with Irish Prime Minister Leo Varadka, who said "time is running short" to reach a deal.
Luxembourg's Prime Minister Xavier Bettel also said time was "getting short", adding: "We both need to find a compromise."
The Netherlands' Mark Rutte warned of a failure to reach agreement, saying: "As long as there is no deal, there is the risk of 'no-deal'."(FA)