The statement by the 28 European Union member states meeting in Brussels comes after Turkey's arrest of two Greek soldiers, and its promise to prevent the internationally-recognised Greek Cypriot government from exploring for oil and gas.
"The European Council strongly condemns Turkey's continued illegal actions in the Eastern Mediterranean and the Aegean Sea and underlines its full solidarity with Cyprus and Greece," the draft conclusions said.
The draft "calls on Turkey to cease these actions and respect the sovereign rights of Cyprus to explore and exploit its natural resources in accordance with EU and international law."
The statement shows firm support for Greece and Cyprus -- which have so far been among the EU countries most reluctant to endorse a separate EU summit condemnation of a nerve agent attack on a former Russian agent on English soil.
The draft urged Turkey to normalise relations with Cyprus, divided since 1974 when Turkish troops invaded and occupied the northern third of the island in response to a Greek military junta-sponsored coup.
A standoff over exploiting energy resources in the region risks further complicating stalled efforts to reunify Cyprus after UN-backed talks collapsed last year.
In recent weeks Turkish warships blocked an Italian drillship from exploring for gas in the east Mediterranean island's waters.
The leaders also expressed "grave concern over the continued detention of EU citizens in Turkey" and called for these issues to be resolved through dialogue with the EU member states.
'Difficult and sensitive'
Two Greek soldiers were arrested on March 2 for entering a military zone in the northern Turkish province of Edirne and are waiting for their case to be heard.
Ties between Athens and Ankara are strained by the Greek failure to extradite eight Turkish troops who escaped Turkey by helicopter on the night of the July 2016 attempted overthrow of President Recep Tayyip Erdogan.
Turkish tensions with Greece and Cyprus are part of a wider plunge in relations since Brussels denounced Ankara over its post-coup crackdown.
Turkey has expressed increasing anger over its long-stalled bid to join the EU, mainly over human rights concerns.
It was not clear whether the summit denunciation could derail an EU-Turkey summit in the Bulgarian resort of Varna on Monday aimed at improving strained ties.
An EU diplomat appeared to suggest Wednesday that the summit would go ahead although it will be "difficult and sensitive" because of the many disputes.
The diplomat said on condition of anonymity that the goal would be to keep "pragmatic strategic cooperation."
The EU sees Turkey as a strategic partner in the fight against Islamic extremism and its efforts to stop Syrian and other asylum seekers from flooding into Europe and destabilising the bloc under a 2016 aid-for-cooperation deal.
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