European Council President Donald Tusk has warned Theresa May there is "no time to lose" in the Brexit negotiations.
With talks due to start in Brussels in ten days time, Mr Tusk said it was their "urgent task" to get on with the negotiations in "the best possible spirit".
In a letter to the Prime Minister congratulating her on her reappointment, he said the two-year time frame set out under Article 50 of the EU treaties left no room for delay.
"Our shared responsibility and urgent task now is to conduct the negotiations on the UK's withdrawal from the European Union in the best possible spirit, securing the least disruptive outcome for our citizens, businesses and countries after March 2019," he said.
"The time-frame set by Article 50 of the Treaty leaves us with no time to lose. I am fully committed to maintaining regular and close contact at our level to facilitate the work of our negotiators."
European Commission president Jean-Claude Juncker said he hoped there would be no further delay to the negotiations.
"As far as the commission is concerned, we can open negotiations tomorrow morning at half-past nine," he said.
"I do hope that the result of the election will have no major impact on the negotiations we are desperately waiting for."
Earlier, Brussels' chief negotiator Michel Barnier has said the talks would begin when Britain was ready, suggesting he would consider a short delay.
In a message released on Twitter, Mr Barnier said: "Brexit negotiations should start when UK is ready; timetable and EU positions are clear. Let's put our minds together on striking a deal."
There was clear frustration with the EU at the failure of the election to deliver a decisive result.
The European Parliament's Brexit co-ordinator, Guy Verhofstadt, said: "Yet another own goal, after Cameron now May, will make already complex negotiations even more complicated."
Germany's European Commissioner Gunther Oettinger said "a weaker partner weakens the whole thing", while if both sides were strong "you get results more quickly".
He told German radio that the timetable for completing the talks was "ambitious" and Britain had already lost a lot of time by delaying its Article 50 letter and then calling an election.
"We will have to see whether the negotiation chief will remain the same, how the relevant ministers will look," he said.
"Therefore I am expecting uncertainty, because it has an effect on everything. It has an effect on tariff negotiations, on contract negotiations in business and in politics."
German foreign minister Sigmar Gabriel said he hoped the election result would be seen as a message that the British people do not want a hard Brexit.
He urged the Government to "reconsider whether it's really good for Great Britain to withdraw from the European Union in this way".
He said he hoped the new Government was one "with which we can conduct serious negotiations and if possible keep Great Britain as close as possible to the European Union".