Brexit Secretary David Davis had wanted trade talks to take place in parallel with negotiations on the divorce bill from Brussels and had previously warned that the dispute would be "the row of the summer". German Chancellor Angela Merkel called them "a good start".
More broadly, Brexit talks will have to address a range of regulatory issues, including laws about worker rights, climate and agriculture.
"We must first tackle the uncertainties caused by Brexit", Barnier said, citing the rights of European Union citizens in Britain and the possible impact on the open border between Northern Ireland and Ireland. May also promised to cut the burdensome bureaucracy such paperwork can involve, the official said.
With these tight negotiations and UK's current domestic crisis it does appear that today will be the start of a very long and arduous 21 months, if not longer.
Given the floor for 10 minutes at the end of a Brussels summit dinner, her first since she launched the two-year withdrawal process in March, May outlined five principles, notably that no European Union citizen resident in Britain at a cut-off date would be deported.
Merkel said in Brussels on Thursday that the Brexit talks will be conducted quickly and "we will do everything to continue succeeding, as we have so far, in keeping the 27 member states together". These facts are signs that she might face pressure to a secure a soft Brexit deal as opposed to her original plan of a hard Brexit which would have meant she would have more control over immigration and law-making.
Donald Tusk, the former Polish prime minister chairing a summit of European Union leaders in Brussels attended by British Prime Minister Theresa May, spoke of the revival of discussion in Britain since May lost her parliamentary majority on June 8. Our aim is to have one week of negotiations every month.
That was, she told them, "a fair and serious offer", a British official said.More news: Timberwolves take Markkanen with No. 7 pick for Bulls
"So who knows? You may say I am a dreamer but I'm not the only one", Tusk continued, quoting a lyric from the late John Lennon's "Imagine". "And I am not the only one", Michel said.
Brexit negotiations began on Monday.
He added that "What we also need is certainty, for our companies in Belgium, in Europe".
This would provide a "smooth path" from "where we are now" to where the United Kingdom would end up post-Brexit, he said.
Hammond's more frequent and pointed interventions in the Brexit debate have come amid mounting evidence that the economic situation in Britain has worsened just as it has gotten brighter for the rest of the EU.
Asked about the timeline of Brexit negotiations, Mr Varadkar said: "I think what's much more important than the timetable is the outcome".
The announcement was made alongside the start of discussions with the European Union on Brexit on June 19.
He pushed at the summit for joint European defence, a joint budget for countries that use the euro and a tougher stance against the USA and China on trade. Recalling his own past as a dissident who saw Soviet communism collapse, he told reporters: "Miracles do happen". European Union leaders are gathering for a two day summit to weigh measure.