EU president Donald Tusk warned Tuesday that hard work lay ahead to finalise the deal, after Cyprus threatened to derail it over long-standing disagreements with Turkey.
Tusk held talks in Nicosia in an attempt to win Cyprus' backing for the proposal, which has been hailed as a "game-changer" for European countries buckling under the wave of new arrivals.
EU and Turkish leaders last week agreed a tentative plan that would see new migrants landing in Greece sent back to Turkey. For each Syrian refugee returned, the EU would resettle one from a Turkish camp.
Cyprus has expressed reservations, not least because longtime adversary Turkey expects the accord to further its EU membership bid and ease visa requirements in the passport-free Schengen area.
Top United Nations officials on refugees and human rights have also questioned whether the plan would be legal.
Tusk conceded this was an issue and it was "not an easy task" to make the proposal legally sound and acceptable to all 28 EU members.
"It is clear that there is still hard work to be done," Tusk said after flying to Ankara, adding there was "a catalogue of issues" to address before the talks on Thursday and Friday.
German Chancellor Angela Merkel, who has championed the proposal, will also lay out her position before the Bundestag.
Paris on Tuesday insisted that Turkey will not be allowed to dictate terms at the meeting.
Prime Minister Manuel Valls said France will tell Turkey it wants "more efficient" cooperation on the migrant crisis, but will warn against any attempt at "blackmail".
Czech President Milos Zeman also lashed out at Ankara on Tuesday, claiming that Ankara was seeking billions of euros more in EU aid.