(AFP) - European Union leaders agreed Friday to open crucial talks on a future relationship with Britain once it leaves the bloc, but warned it would be "dramatically difficult" to reach a deal before Brexit in 2019.

The leaders of the 27 other member states met without British Prime Minister Theresa May to endorse an interim deal on the terms of the separation, and approve the next stage of discussions.

EU President Donald Tusk said afterwards that the bloc would open "exploratory contacts with the UK to get more clarity on their vision" for ties after Brexit.

But while talks will begin in January on a post-Brexit transition period, the EU's guidelines state that actual negotiations on the future relationship -- including trade -- will not start until March.

Tusk said the next stage would be even harder than the tortuous six months of negotiations that led to last Friday's interim accord on Britain's financial settlement, expatriate rights and the Irish border.

Asked if a final deal could be achieved by the time Britain leaves on March 29, 2019, he cautioned that it was "still realistic and of course dramatically difficult".

May, who had left the summit in Brussels after dinner on Thursday night, expressed on Twitter her thanks to Tusk and European Commission President Jean-Claude Juncker.

"Today is an important step on the road to delivering a smooth and orderly Brexit and forging our deep and special future partnership," she said.

As he arrived for the talks, Juncker -- who sealed the deal with May on December 8 after tense all-night talks -- said the British premier had made "big efforts".

But he also warned that the next stage "would be much harder than the first phase, and the first phase was very hard".

German Chancellor Angela Merkel added that while progress had been made, the negotiations ahead would be "even tougher".

She had warned earlier that "there remain many issues to be solved and we don't have much time".

- 'Well on the road' -

EU leaders took just 15 minutes to approve last week's deal and negotiating guidelines, saying there had been "sufficient progress" and agreeing that the second phase of Brexit talks could begin.

May said Friday that negotiations on Britain's future relationship with the EU would begin "straight away".

"I am pleased that it has been agreed that we should make rapid progress on an implementation period, which will give certainty to businesses and individuals," she said.

"There is still more to do but we are well on the road to delivering a Brexit that will make Britain strong, prosperous and secure."

British officials are hoping for a deal by March on a two-year transition out of the bloc, during which their relationship would largely stay the same.

They also want to agree a new trade deal before Brexit, though the EU guidelines state this cannot be signed until after Britain leaves the bloc -- and officials warned it could take years to do so.

Options for a future relationship include following the model of a recent EU-Canada trade deal, or Norway's membership in the European Economic Area.

An EU source said Friday that Britain would also be able to negotiate trade deals with other non-EU countries during the transition but not sign them -- a condition London is likely to contest.

- 'Test of EU unity' -

May received polite applause when she addressed EU leaders at a summit dinner on Thursday, and several of her counterparts praised her role in securing progress.

She has struggled to assert her authority in recent months, and just hours before the summit had suffered a humiliating parliamentary defeat over her Brexit plans thanks to rebellious lawmakers in her own Conservative Party.

But in a welcome move on Friday, these same rebels tabled a new, more conciliatory, amendment on the exact timing of Brexit to the draft withdrawal legislation, which should avert another House of Commons vote loss for May next week.

It proposes allowing ministers to amend the date and time of Brexit, which the government wants to fix in law as 11pm of March 29, 2019 but rebels had opposed.

Hungarian Prime Minister Viktor Orban said she was "a tough leader in the interest of Britain".

Dutch Prime Minister Mark Rutte, who earlier described May as a "formidable political operator", said the British had been "smart" by trying to negotiate directly with individual EU leaders, while noting that the Europeans had held their position.

But Tusk has warned that the next phase of talks will be the "real test of our unity".

© Agence France-Presse