The EU's negotiating guidelines state they will start talks on a post-Brexit transition in January but will not begin trade talks until March, calling for more clarity about Britain's goals.
On the rights of the three million Europeans living in Britain and one million Britons in the EU, the issue of whether the European Court of Justice will keep jurisdiction over them remains a key sticking point.
"A fair deal is far better than no deal," Barnier told an EU panel on Brexit, repeating the phrase twice in English.
According to the statement issued on Thursday, the EU and the UK are set to begin negotiations on Article 50, which was triggered on March 29 and sets out the procedure for withdrawing from the 27-member bloc
"President Trump emphasised his commitment to the United States-United Kingdom special relationship and underscored that he looks forward to working with the Prime Minister on shared goals and interests in the years to come," the White House said in a statement
"We are ready for the negotiations. We want to do it quickly, respecting the calendar," Merkel said during a visit to Mexico.