UK Prime Minister Theresa May has said the EU must treat the UK with "respect" in Brexit negotiations.
In a statement at Downing Street she said for EU leaders to reject her plan with no alternative at this "late stage of negotiations" was "not acceptable".
Progress could not be made without "serious engagement" on future trade relations and the Irish border.
At an EU summit on Thursday, European Council President Donald Tusk said Mrs May's plan "will not work".
The UK is due to leave the EU on 29 March 2019.
The two sides are trying to reach a deal in time and want to avoid a hard border - physical infrastructure like cameras or guard posts - between Northern Ireland and the Irish Republic but cannot agree on how.
This week's summit in Salzburg saw the prime minister attempt to sell her Chequers plan directly to EU leaders.
Mrs May says her plan for the UK and EU to share a "common rulebook" for goods, but not services, is the only credible way to avoid a hard border between Northern Ireland and the Republic of Ireland.
But speaking after talks with the prime minister, Mr Tusk said while there were some "positive elements" in Mrs May's proposals, EU leaders had agreed that "the suggested framework for economic co-operation will not work, not least because it is undermining the single market".
Speaking on Friday, the prime minister said: "Throughout this process I have treated the EU with nothing but respect. The UK expects the same, a good relationship at the end of this process depends on it.
"At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and counter proposals.
"So we now need to hear from the EU what the real issues are and what their alternative is so we can discuss them. Until we do, we cannot make progress."
She said the two sides were still "a long way apart" on two big issues: the post-Brexit economic relationship between the UK and EU, and the "backstop" for the Irish border, if there is a delay in implementing that relationship.
The two options being offered by the EU for the long-term relationship - for the UK to stay in the European Economic Area and customs union or a basic free trade agreement - were not acceptable, she added.
The first would "make a mockery of the referendum" she said, while the second would mean Northern Ireland would be "permanently separated economically from the rest of the UK by a border down the Irish Sea."