"Our shared responsibility and urgent task now is to conduct the negotiations on the U.K.'s withdrawal from the European Union in the best possible spirit, securing the least disruptive outcome", EU Council President Donald Tusk wrote in a congratulatory message to May.
May Friday insisted that she would stick to the Brexit timetable.
Voters dealt Prime Minister Theresa May a devastating blow in a snap election she had called to strengthen her hand in Brexit talks, wiping out her parliamentary majority and throwing the country into political turmoil.
Current plans to start Brexit negotiations in the week of June 19 may have to be delayed, experts said, adding that when the talks do begin there could be a very different approach from the "hard Brexit" advocated by May that would involve leaving Europe's single market and curbing European immigration.
What can not easily be delayed, however, is the date of Britain's departure from the European Union, which is due to take place exactly two years after the triggering of the Article 50 Brexit process on March 29 2019, whether or not a withdrawal deal has been reached. "We know when they must end", said Mr Tusk. "Let's put our minds together on striking a deal", he said on Twitter.
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"We are ready for the negotiations".
The prospect of a hung Parliament would throw serious doubt over Brexit negotiations, due to begin in earnest in just 10 days.
He said: "The British will now have to set up a new team".
In the wake of last year's Brexit referendum, called and lost by Prime Minister David Cameron, Britain's Conservative party took a long time to reorganize itself before it finally triggered the Brexit negotiations on March 29. There is a new government, perhaps a minority government, which will be dependent from day to day on shifting majorities in Parliament, in the lower house.
He told German radio station Deutschlandfunk that in negotiations, "a weaker partner weakens the whole thing", while if both sides were strong "you get results more quickly". It has an effect on tariff negotiations, on contract negotiations in business and in politics. "A weakened partner weakens the whole negotiation".
Angela Merkel has said Brexit negotiations should go ahead as scheduled in nine days' time - despite the United Kingdom being plunged into political turmoil by the General Election.