The EU's top diplomat Federica Mogherini said Tuesday that Turkey would only get visa-free travel to the bloc once it has met all the required criteria.

Turkey has demanded its citizens be allowed to enter the European Union's passport free Schengen zone without a visa by June, in exchange for it taking back migrants from Europe.

But the EU insists that Turkey must meet 72 conditions before allowing visa-free travel, of which it is believed to have fulfilled about half.

‘On free travel, this will be done only once all the criteria are respected, as for all countries with which we negotiate free travel for a limited period,’ EU foreign policy chief Mogherini said on France Inter radio.

‘It was the case with Georgia, it was the case with Ukraine, it is a discussion we are having with Kosovo. There are very strict, technical criteria that must be put in place, a very severe verification must be carried out to apply this measure.’

The EU struck the deal with Turkey to send back all ‘irregular’ migrants which arrive in Greece after March 20 in a bid to halt mass migration which has created enormous strain in Europe.

Two sets of deportations expelling 325 migrants from Greece took place three weeks ago, but there has been no movement since.

The operation has been hampered by last minute asylum applications and Turkey has also sounded the alarm several times against the EU failing to keep its side of the bargain.

The accord is awash with legal and moral concerns, and critics have accused the EU of sacrificing its values and overlooking Turkey's growing crackdown on free speech in order to secure the deal.

The deal also promises to fast-track Turkey's accession to the EU.

Mogherini said resuming talks on Turkey's accession was ‘the only way we can help Turkey modernise its state (and) respect fundamental rights including press freedom ... and also hold a larger conversation for example on relaunching peace talks with the Kurds.’

European Council president Donald Tusk said last week that ‘Europe must set clear limits to its concessions. We can negotiate money, but never our values.’

‘Our powerlessness could lead to a temptation to blackmail Europe,’ he warned.

The deal has already sharply reduced the number of people crossing from Turkey to Greece, though the International Organisation for Migration has said the numbers are ‘once again ticking up’, possibly as smugglers get more creative.

If Ankara meets its side of the agreement, the European Commission has promised to recommend next month that EU states approve visa-free travel for Turks.