The 27 leaders met in Brussels today to formally adopt negotiating guidelines for talks on the future UK-EU relationship, and agree to a 21-month transition period when Britain leaves the bloc in March 2019.
The Prime Minister said over dinner last night that it was their duty to show "energy and ambition" in forging a future relationship which was in the interests of both Britain and Europe.
As she left the leaders' summit in Brussels, Theresa May said she believed there was a "new dynamic" to the negotiations, and reiterated her commitment to offer answers on the Irish border. May said on Friday: "We will now be sitting down and determining those workable solutions for Northern Ireland but also for our future security partnership and economic partnership".
But the imposition of a new deadline for progress on the Irish issue steps up the pressure on Britain to find a solution to one of the thorniest problems of Brexit.
European Union leaders agreed that the transition period would begin after the 29 March 2019 Brexit deadline and last until the end of 2020.
Prime Minister Theresa May said she believed there was a new "spirit of co-operation and opportunity".
Speaking as he headed into the summit, Michel Barnier, Brussels' chief Brexit negotiator, said the European Union was "crossing a decisive point in this hard and extraordinary negotiation". May said the deal would give "certainty to people and businesses" and give them "clarity to plan for their future" Both sides say they do not want to go back to border checks between the Republic of Ireland and Northern Ireland - as was the case during decades of violence in the British province.
"The Council has also endorsed its guidelines for our negotiations for that future relationship".
Mr Rutte added: "Let's use the time between now and June to negotiate and then to see whether there's any movement on the red lines".
However, the 27 insisted in their guidelines on the future trade deal that negotiations could only progress once the United Kingdom provides a legally watertight alternative to its "backstop" solution of keeping Northern Ireland in regulatory alignment with the EU.
The 27 EU states, without Britain, approved a clause past year that "after the United Kingdom leaves the Union, no agreement between the EU and the United Kingdom may apply to the territory of Gibraltar without the agreement between the Kingdom of Spain and the United Kingdom".
Last-minute wrangling by Spain has led to the inclusion of a reference to the EU's position on Gibraltar.
"As the sector hardest hit by Brexit, a time-limited transition period has been at the top of FDF's negotiation wish-list".