The EU said it was ready for a closer relationship with Turkey, but only if recent de-escalation in the eastern Mediterranean was sustained and Ankara was willing to engage constructively with Brussels.
Brussels warned Turkey it would use the “instruments and options at its disposal” to protect EU member states if Ankara was unable to abstain from provocation or illegal actions.
The offer came after Thursday’s European Council meeting, where the EU’s often uneasy relations with its neighbour Turkey were a major part of talks.
Tension soared last year after the EU backed member states Cyprus and Greece in a dispute with Turkey over maritime borders and drilling activities in the eastern Mediterranean. The bloc levied sanctions on several Turkish people and entities as a result, but has not gone any further after Ankara backed down.
Brussels has been highly critical of recent domestic repression in Turkey and condemned President Recep Tayyip Erdogan last year when he questioned the mental health of French President Emmanuel Macron.
There are signs Ankara is more willing to adopt a conciliatory approach, however, as it restarted exploratory talks with Greece and halted drilling activities in the Mediterranean that the EU described as illegal.
The European Council said it was ready to enhance co-operation with Turkey in a number of areas in a “phased proportionate and reversible manner”, as long as the goodwill continued.
This included intensifying talks on a reformed EU-Turkey customs union and high-level dialogues on issues such as public health, climate change, counter-terrorism and wider regional issues.
Turkey wants to update a deal struck five years ago to stop large-scale migrant arrivals in the EU, many of them fleeing the war in Syria via Turkey, in return for billions of euros in aid.
The bloc has so far refused to reopen the agreement but the summit told the European Commission to come up with a proposal on more funding for Turkey for housing millions of refugees.
"We think it is important to keep on going with the support in this humanitarian cause concerning the Syrian refugees in Turkey," Ursula von der Leyen, President of the European Commission said.
The EU, however, reiterated its alarm at recent domestic incidents in Turkey, including attempts to ban a major opposition political party, and its withdrawal from a treaty on violence against women.
“Rule of law and fundamental rights remain a key concern. The targeting of political parties and media and other recent decisions represent major setbacks for human rights and run counter to Turkey’s obligations to respect democracy, the rule of law and women’s rights.
“Dialogue on such issues remains an integral part of the EU-Turkey relationship,” a statement said.
The bloc’s foreign policy chief Josep Borrell had earlier warned the situation remained fragile, despite positive developments in recent months.
European Council President Charles Michel, who chaired the meeting, said there was "a clear framework and we hope, we really hope, it will be possible to improve the relationship with Turkey.
"But we remain cautious and remain careful."
He said EU officials were in contact with Turkey to discuss the possibility of a visit in April.
"We need contact with Turkey at all levels and also to talk about both the controversial and common interests. We are now taking a first step and giving a mandate to further develop relations and then want to take decisions in June," German Chancellor Angela Merkel said., referring to the next European Council.