European Council President Donald Tusk has warned British Prime Minister 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 UK 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 Union leaders are braced for a delay in the talks following Mrs May's shock loss of her majority in the snap British election, with some EU officials raising the risk of negotiations failing.
European Commission president Jean-Claude Juncker said Brussels was "desperately" waiting for the talks to start.
"I hope that we will not experience a further delay in the conclusion of these negotiations," Mr Juncker told reporters in Prague. "As far as the commission is concerned we can open negotiations tomorrow morning at half past nine."
Earlier, the EU chief negotiator Michel Barnier said the bloc's stance on Brexit and the timetable for the talks are clear, adding the divorce negotiations should only start when Britain is ready.
"Brexit negotiations should start when UK is ready; timetable and EU positions are clear. Let's put our minds together on striking a deal," Michel Barnier said.
Congratulations @theresa_may. Our responsibility now is to secure least disruptive #Brexit. No time to lose. https://t.co/bOOzzwr82k
— Donald Tusk (@eucopresident) June 9, 2017
Brexit negotiations are due to start on Monday 19 June, however German MEP Guenther Oettinger said it was unclear if negotiations could begin on that date as the talks would be more uncertain without a strong negotiating partner.
"We need a government that can act," Mr Oettinger told German broadcaster Deutschlandfunk.
With a weak negotiating partner, there's the danger than the negotiations will turn out badly for both sides...I expect more, more uncertainty now.
His French colleague Pierre Moscovici said the result would affect the negotiations but declined to be drawn on whether the EU executive hoped Britain might ask to stay.
He told Europe 1 radio that Brexit was supported by most of the last parliament following the referendum a year ago and that the timetable for leaving in 2019 was not "optional" but fixed in treaty law.
Britain must leave the EU within two years of triggering Article 50, which it did in late March.
Germany's deputy foreign minister said there was no time to lose in negotiating Britain's departure from the European Union.
"We need to get started on the negotiations as soon as possible because time is ticking," said Michael Roth - a member of the country's Social Democrat Party, which is the coalition partner of German Chancellor Angela Merkel.
"Regardless of the question of who will form a government in Britain, time is ticking... We have less than two years to negotiate the exit ... so we should not waste any time now," he added.
French Prime Minister Edouard Philippe said that the British election result was a surprise but did not change the country's decision to leave the European Union.
"The British have spoken, they have voted, and have given the Conservative party a majority, albeit a simple majority, which is something of a surprise," Philippe told Europe 1 radio.
But he added: "I don't think we should read these results as calling into question the stance on Brexit which was clearly expressed by the British people."
Mr Philippe, who only took office in May, said the British election "had relatively little to do with Brexit and far more to do with domestic issues, for example linked to security" following the terror attacks in Manchester and London.
"I don't think we can read anything into this vote than a desire expressed by the British to choose the Conservative Party, but with less intensity than we thought beforehand," he said.
The president of the Socialists and Democrats grouping in the European Parliament, Italian MEP Gianni Pitella, said: "It's a disaster for May. Her huge gamble has backfired spectacularly. She has no credibility in UK or Europe. She should resign.
"May's wasted enough time. Negotiations must start. We want a positive relationship but rights and benefits can't be the same for UK post-Brexit."
Meanwhile a number of other European politicians took to Twitter to give their opinion on the result.
Former Finnish premier Alexander Stubb said: "Looks like we might need a time-out in the Brexit negotiations. Time for everyone to regroup."
Elsewhere the chairman of Germany's SDP party Martin Schultz congratulated Labour.
What a race! Congratulations to @jeremycorbyn and @UKLabour!
— Martin Schulz (@MartinSchulz) June 9, 2017
Just talked to Jeremy Corbyn on the phone. We agreed to meet very soon.
— Martin Schulz (@MartinSchulz) June 9, 2017
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European leaders have largely given up considering the possibility that Britain might change its mind and ask to stay.
Most now appear to prefer that the bloc's second-biggest economy leave smoothly and quickly. To halt the Brexit process now would require the consent of the other member states.
Mrs May, who had campaigned against Brexit last year but took over the Conservative party after David Cameron lost last June's Brexit referendum, delivered her terms for withdrawal in March.
These include a clean break from the EU's single market and customs union. Mrs May then called a snap election hoping for a bigger majority to strengthen her hand in negotiations.
That was also the broadly desired outcome in Brussels, where leaders believed that a stronger May would be better able to cut compromise deals with the EU and resist pressure from hardline pro-Brexit factions in her party which have called for Britain to reject EU terms and, possibly, walk out without a deal.
Elmar Brok, a prominent German conservative member of the EU parliament, said Europeans would be disappointed Mrs May had failed to gain the majority that could have helped her override her party hardliners: "Now no prime minister will have that room for manoeuvre," he said.
"Which is what makes things so difficult."
Fear of collapse
The other 27 governments are particularly concerned that a breakdown in negotiations could lead to Britain ceasing to be a member on 30 March 2019, as laid out in Article 50 of the EU treaty, without negotiating the kind of divorce terms that would avoid a chaotic legal limbo for people and businesses.
That would also make it improbable that Britain could secure the rapid free trade agreement it wants with the EU after it leaves.
In a note to clients, UBS wrote that the relative strength of hardline pro-Brexit groups in a weak Conservative government could make a breakdown in talks more likely and make it harder to reach a trade deal: "A tighter political balance could make it easier for Eurosceptics ... to prevent the government from offering the compromises needed to secure a trade deal."
Talk in Britain that a different ruling coalition could seek a "softer" Brexit than Mrs May has proposed, possibly seeking to remain in the single market, is also problematic for the EU.
While the 27 would quite possibly be willing to extend to Britain the same kind of access to EU markets that they offer to Norway or Switzerland, they have made clear that that would mean Britain continuing to pay into the EU budget and obey EU rules, including on free migration across the bloc, while no longer having any say in how the Union's policies are set.
EU leaders question how any British government could persuade voters to accept such an outcome and so would be wary of starting down the path of negotiating it for fear of ending up without a deal that both sides could ratify in 2019.
Siegfried Muresan, spokesman for the European centre-right party whose dominant leader is German Chancellor Angela Merkel, was scathing, saying on Twitter that Mrs May had followed Mr Cameron in risking the "future of the country for personal political gain".
She had, he said, "played with fire" in binding Britain to the two-year deadline for Brexit talks and had now "got burned".