EU chiefs to see Erdogan in Turkey next week
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The trip comes after EU leaders agreed at a summit on Thursday that they were ready to improve cooperation with Ankara if Erdogan maintains a current "de-escalation" after a spike in tensions over the eastern Mediterranean last year.
The bloc has been encouraged by the resumption of talks involving Turkey and Greece over a disputed maritime border and by plans to restart UN peace efforts for divided EU member state Cyprus.
But leaders remain deeply wary of Erdogan and there are major concerns over Ankara's recent moves to shut down an opposition party and its departure from a treaty on violence against women.
Last week's summit conclusions said the 27-nation bloc was "ready to engage with Turkey in a phased, proportionate and reversible manner to enhance cooperation in a number of areas of common interest".
But that was only if "the current de-escalation is sustained and that Turkey engages constructively".
The EU has warned it could slap sanctions on its southeastern neighbour if it backtracks.
On the table for discussion is a raft of key Turkish ambitions including modernising a customs union with the EU, liberalising visa rules and more support for hosting millions of refugees from Syria.
Turkey is pressing Brussels to update a deal struck five years ago to stop large-scale arrivals of migrants in the EU, many of them fleeing war in Syria, in return for billions of euros in aid.
The bloc is refusing to reopen the agreement but last week's summit told the European Commission to come up with a proposal on more funding for Ankara.
EU leaders said they will discuss Turkey's progress at a summit in June and could take "further decisions" on cooperation.
The bloc's members are divided over their approach to Ankara, with Cyprus, Greece and France urging a tough line while others, led by economic powerhouse Germany, pushing for more engagement.