"We were in the European Union for reasons of utility rather than emotion". Britain remains our neighbour, like the European Union is for Britain.
German Chancellor Angela Merkel, Mr Tusk and European Commission president Jean-Claude Juncker said the United Kingdom would remain a "close and committed ally".
German officials have made clear in recent months that they do not believe there is time to negotiate a bespoke transitional agreement for Britain that would come into force immediately after Brexit.
There was "no reason to pretend that this is a happy day" in Brussels or London, he added.
Both sides have also said they are keen to resolve the status of more than three million European nationals living in Britain after Brexit, and one million British expats living in the EU.
She also underlined global cooperation with Italy in La Repubblica and referred to an estimated 600,000 Italian nationals living in Britain and three million British tourists who visit Italy every year.
"If the outcome of the negotiations is not in conformity with the points and conditions we have made public today, yeah, then we will use our veto power, it is clear", he said.More news: Last-shot practice pays with Final Four for North Carolina
And Mr Davis disputed claims that Theresa May tried making a trade-off between security and commerce by mentioning the crime-fighting measures alongside a trade deal in her letter.
He said he welcomed "the constructive approach" in May's letter and hoped the relationship between the two countries would be "as positive and mutually beneficial as possible even after withdrawal".
Tusk held up the letter signalling the UK's intention to leave the European Union on Wednesday, saying "We already miss you". "A strong, independent country needs control of its own laws. We need each other".
Davis said the method of transferring European Union law into British law was a mirror to how he saw trade negotiations playing out over two years.
Brexit secretary David Davis and his team insisted that counterparts in Brussels received Britain's Article 50 letter positively on Wednesday.
Brexit minister David Davis said there would be no sudden drop in numbers, as it would take years to fill low-skilled jobs in hospitality, health and agriculture now done by immigrants. Parliament president Antonio Tajani told a news conference that if Britain chose to reverse course, "it can not do it alone (as) all member states need to decide whether it is possible (too)".
France has insisted that the United Kingdom must first sort out the terms of its exit from the European Union before talks can move on to future relationships.