"The tensions in and challenges for Turkey cannot be solved with guns," EU President Tusk told reporters during an Asia-Europe summit in Mongolia.
"Military coups have no place in modern Turkey. There is no alternative to democracy and the rule of law."
The comments followed a joint statement by Tusk, European Commission head Juncker, and EU foreign policy head
Federica Mogherini calling for "a swift return to Turkey's constitutional order".
"Turkey is a key partner for the European Union. The EU fully supports the democratically elected government, the institutions of the country and the rule of law," it added.
EU representatives at the gathering met earlier in the day to discuss the unfolding situation.
Brussels will be watching with deep concern as events progress in Turkey, a key partner on its south-eastern flank which has been trying to join the EU for many years without success.
Turkey is also a crucial partner for the EU because of the controversial deal they signed in March to tackle the migration crisis.
Under the deal, Ankara agreed to take back migrants and refugees from the Greek islands and to stop people crossing the Aegean Sea. In return it is to get aid and visa-free travel for 80 million Turks to the EU.
The bloc overcame its aversion to Erdogan's increasingly authoritarian rule, which has received sharp criticism from the EU, to sign the deal.
Tusk said it was "too early to speculate" on the potential consequences of the coup attempt.
"The key question will be what kind of Turkey comes out from this crisis," he said, adding that how the country deals with the consequences "will be crucial not only for Turkey but the whole region and of course EU-Turkey relations."
"Our hope and intention is of course to keep Turkey as a key partner," he said.
Nato and US President Barack Obama have also backed the country's democratic institutions following the coup attempt.
Turkey will now likely dominate an EU foreign ministers' meeting on Monday which will also be attended by US Secretary of State John Kerry.