However, European leaders will not discuss how Britain should leave the European Union until London triggers the formal leaving mechanism Taoiseach Enda Kenny and Mr Tusk affirmed.
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Technically, EU leaders can not start negotiations on post-Brexit Europe until Britain triggers the Article 50 mechanism for leaving, but Bratislava is widely expected to be a start of talks about the way forward.
Mr Tusk said the Bratislava summit must show that the “political elites in Europe are not detached from reality”.
The Prime Minister has faced accusations of vagueness and contradiction over the Government’s position on remaining in the European single market, but has insisted she will not reveal her negotiating hand “prematurely”.
The minister also stated it would “take a little while” to work out how to disentangle the corpus of European law from United Kingdom law, saying that, although his “starting position” was simply to put all of EU law into British law and “take it from there”, he conceded “it does not quite work like that”.
The UK government has said it does not plan to kick-start the formal two-year European Union exit process until the start of 2017 at the earliest, to give it time to prepare its negotiating position.
“Our goal to establish (the) closest possible EU-UK relations”, Tusk wrote on Twitter before the meeting.
Immediately, it demonstrated that the pressure on British PM to reveal her official position on Brexit continues to be unrelenting.
Despite Mr Davis’s comment, the Prime Minister’s spokeswoman said he was expressing a personal opinion rather than official policy.
Referring to talks at the G20 Summit, May, who met Prime Minister Narendra Modi on the margins of the summit, said: “As we leave the European Union we will forge our own trade deals”.
Jeremy Corbyn, the Labour leader, accused the Government of issuing “contradictory messages” on the issue, exacerbating the “huge uncertainty” about the UK’s future.
May used her first worldwide trip to China this week to outline the first details of what she wants from Brexit after nearly 52 percent of Britons voted to leave the European Union in June.
“As spokesman of the German government, I am not going to judge who the British prime minister holds talks with”, Steffen Seibert told journalists in Berlin.
Davis, addressing parliament for the first time since he was appointed after the vote, said the country could restore control over immigration and still get access to the EU’s single market because it was not in Brussels’ interest to hurt trade.
Triggering Article 50, which May has said she will not do this year, leads to a two-year process of exiting the 28-member bloc.
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“We discussed the outcomes from those contacts and I urged prioritisation of the vitally important Northern Ireland dimension in the overall Brexit process, with particular focus on the border but also more widely on sustaining the peace and prosperity so painstakingly built up over recent decades”.
