Britain and the European Union began their first formal Brexit negotiations on Monday, under pressure to seal a deal amid disarray in London over whether to go for a "hard" or "soft" divorce.

"Today we are launching negotiations on the orderly withdrawal of the UK from the EU," said the EU's French chief negotiator Michel Barnier as he greeted Brexit minister David Davis at EU headquarters in Brussels.

British Foreign Secretary Boris Johnson expressed confidence that talks on the terms of U.K.'s divorce from the EU would lead to a "happy resolution" that will benefit both sides on the long run, said.

"The whole process will lead to a happy resolution - I think it can be done with profit and with honor for both sides," Johnson said on the sidelines of an EU foreign ministerial meeting in Luxembourg.

"I think the most important thing now is for us to look to the horizon, to raise our eyes to the horizon, think about the future, think about the new partnership - the deep and special partnership - that we want to build with our friends."

He noted that taking such an approach to the talks "will be good for the UK and good for the rest of Europe" in the long run.

While the EU negotiating team led by Michel Barnier has been ready for months, Britain stalled even after it triggered the two-year process on March 29. A snap election early this month, in which Prime Minister Theresa May lost her majority, only added to the problems.

Still, the May's government said in a statement it was "confident it can achieve a bold and ambitious deal that will work in the interest of the whole UK." The EU said it was also looking for a good compromise

Austrian Foreign Minister Sebastian Kurz says: "If we don't succeed both sides will lose."