But, also conscious of Irish worries about a possible political fudge on the issue, he stressed that the backstop must be "legally operational" and said a summit in Brussels on October 18 would be a "moment of truth" for whether a deal was possible before Britain leaves the European Union, deal or no deal, next March.
Looking ahead to that summit, in Brussels on 18 and 19 October, he said: "It is then we shall see whether agreement we are hoping for is in our grasp".
May's former foreign minister, Boris Johnson, attacked May's Brexit plans.
"With goodwill and determination on both sides we can avoid a disorderly exit and find new ways of working together".
'We gave people the opportunity to make a choice.
"There are potentially two approaches: have a joint political declaration which is very much clear to the last point or to have a political declaration which while registering an agreement on a number of issues, leaves a certain space for negotiations in the future on a number of issues".
"A future prime minister could always choose to alter the relationship between Britain and the European Union". 'What we are talking about here is not a border - not a land border, not a sea border.
Failure to reach a deal would imply some upheaval, May acknowledged.
In his pre-summit letter to European Union leaders, Tusk said the meeting will "reconfirm the need for a legally operational backstop on Ireland, so as to be sure that there will be no hard border in the future".
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President about all the aspects connected with the permanent presence of the U.S. armed forces in Poland", Duda said. Trump said it was "ridiculous" because it benefited Russian Federation and was bad for the German people.
It has proposed that Northern Ireland stay aligned with the remaining 27 bloc members after Brexit as part of a "backstop", or insurance policy to avoid the reimposition of border checks.
Johnson also said the EU's technology proposal for the Irish border would mean Northern Ireland being "annexed" by Brussels.
"Our proposal for the backstop on Ireland and Northern Ireland has been on the table since February", Mr Barnier said, switching from his native French to English to get his message over.
Leaders will be asked whether they want to fast-track a plan to beef up the EU's border agency to 10,000 personnel by 2020.
As MAC chairman Alan Manning acknowledged, the report will likely come as a blow to business interests and lobbyists, who make claims including that Britain "will wither away" unless European Union freedom of movement is maintained and companies are given the power to import low-skilled workers from overseas.
It is, however, unclear how goods crossing between the EU and the United Kingdom in Ireland would be monitored if there was no border and if Northern Ireland, as a part of the United Kingdom, leaves both the customs union and the single market.
Johnson wrote in Monday's Daily Telegraph that May's Brexit negotiations were heading for a "spectacular political auto crash" that would leave Britain in "the ditch with a total write-off of Brexit".
He said the Irish "backstop" must be "legally operational" and respect the UK's constitutional integrity, a pledge will reassure the prime minister and her cabinet allies.
"It's ensuring that we get that good deal from the European Union which is good for people in the United Kingdom, wherever they live in the United Kingdom, that's what's important for us".
"Unfortunately, a no-deal scenario is still quite possible".