EU invites President elect to summit ASAP
"We should spare no effort to ensure that the ties that bind us remain strong and durable," they said.
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European Council chief Tusk and European Commission boss Juncker said they wanted to discuss issues including terrorism and Ukraine with Republican nominee Trump after he beat Democratic contender Hillary Clinton.
"We would take this opportunity to invite you to visit Europe for an EU-US summit at your earliest convenience. This conversation would allow for us to chart the course of our relations for the next four years," they said in a letter to Trump.
"Today, it is more important than ever to strengthen transatlantic relations," they said.
Tusk and Juncker added: "Only by cooperating closely can the EU and the US continue to make a difference when dealing with unprecedented challenges such as Da'esh (the Islamic State group), the threats to Ukraine's sovereignty and territorial integrity, climate change and migration."
They also cited a troubled EU-US free trade deal, currently under negotiation, as a strong example of transatlantic unity despite Trump's opposition to such deals.
The EU's foreign policy supremo Federica Mogherini also underlined enduring EU-US ties, while also signalling the need to ensure a stronger Europe.
"EU-US ties are deeper than any change in politics. We'll continue to work together, rediscovering the strength of Europe," she said in a tweet.
Martin Schulz, the head of the European Parliament, congratulated Trump, describing an election campaign "that will not be remembered as America's finest."
"Mr Trump has managed to become the standard-bearer of the angst and fears of millions of Americans. Those concerns must now be addressed with credible policies and proposals," he said in a statement.
"Trump's role in diplomacy and deal-making will be tested from day-one and will require the right mix of responsiblity, restraint and leadership," he added.
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