Erdogan's typically combative comments indicated that Ankara would not sit still if the EU falls short on a number of promises in the deal, including visa-free travel to Europe for Turks by this summer.
Meanwhile, the Vatican confirmed that the pope would next week make a brief, unprecedented trip to the Greek island of Lesbos where thousands of migrants are facing potential deportation to Turkey under the deal.
The March 18 accord sets out measures for reducing Europe's worst migration crisis since World War II, including stepped-up checks by Turkey and the shipping back to Turkish territory of migrants who land on the Greek islands.
In return, Turkey is slated to receive benefits including visa-free travel for its citizens to Europe, promised "at the latest" by June 2016.
Turkey is also to receive a total of six billion euros in financial aid up to the end of 2018 for the 2.7 million Syrian refugees it is hosting.
He told AFP that Turkey still has to fulfil 72 conditions on its side to gain visa-free travel to Europe's passport-free Schengen zone and that the move would also have to be approved by EU interior ministers.
Turkey's long-stalled accession process to join the EU is also supposed to be re-energised under the deal. But Pierini said there were many conditions still to be fulfilled here.
"The worst reading of the EU-Turkey deal would be to imagine that Turkey is about to get a 'discount' on EU membership conditions just because of the refugees," he said.
"Some three million people are being fed on our budget," the president said.
"There have been promises but nothing has come for the moment," he added.
The first transfer of more 200 migrants from the Greek islands of Lesbos and Chios to Turkey took place on Monday.
Officials said Greece was preparing to send around 50 more today unless they applied for asylum at the last minute.
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