Tusk held hastily arranged talks in Nicosia in an attempt to win Cyprus's backing for the proposal, which has been hailed as a "game-changer" for countries buckling under the burden of a mass refugee influx.
But there has been a growing pushback against the deal, with both France and the Czech Republic warning yesterday against attempts by Turkey to "blackmail" Europe.
Cypriot President Nicos Anastasiades said his country would not accept "Turkish demands without (the) implementation of Turkey's long-pending obligations," including Ankara's official recognition of the Cyprus government.
Cyprus has expressed reservations, not least as its longtime adversary Turkey expects the accord to lead to the opening of new chapters in Ankara's EU membership bid and the easing of visa requirements in Europe's passport-free Schengen area.
From Nicosia Tusk flew on to Ankara for talks with Turkish Prime Minister Ahmet Davutoglu, saying afterwards it was "not an easy task" to make the proposal legally sound and acceptable to all 28 EU members.
The UN's top officials on refugees and human rights questioned whether the plan would be legal and Tusk conceded this was an issue that still had to be worked out.
Paris yesterday insisted that Turkey will not be allowed to dictate terms at the summit.
France will tell Turkey it wants "more efficient" cooperation on the migrant crisis, but will warn against any attempt at "blackmail", Prime Minister Manuel Valls said.
"Impolite people like myself call that blackmail," he told reporters.
