Last month's EU-Turkey deal on tackling the migrant flow has begun to produce results, a top EU official has said.
"We have seen a sharp reduction of the illegal migration flows," European Council President Donald Tusk said.
In Turkey, he praised the government as "the best example in the world on how to treat refugees", despite criticism by rights groups of the agreement.
Turkish PM Ahmed Davutoglu reiterated the EU should now implement visa-free travel for Turks as part of the deal.
Mr Davutoglu said his country had fulfilled its part of the agreement and that the issue of the visa waiver for entering the EU's Schengen area was "vital" for Turkey.
The deal says Turkey must meet 72 conditions by 4 May to earn access. Diplomats say only half of those points have been met so far.
Earlier on Saturday, Mr Tusk and German Chancellor Angela Merkel visited a migrant camp on the Turkish-Syrian border.
The goal of the deal was to deter migrants, mainly Syrians and Iraqis, from making illegal crossings - mainly by sea - between Turkey and Greece, an EU member.
The UN refugee agency and other rights organisations have voiced concerns about the agreement.
At a joint news conference in the southern city of Gaziantep near the border with Syria, Mr Tusk said: "Our return operations are working in tandem with resettlements of Syrian nationals from Turkey to EU member states, demonstrating the desired shift from illegal to legal migration."
"No-one has a right to lecture Turkey on what it should be doing," he added.
Mr Davutoglu said "the decrease (in numbers) is evidence that the mechanism that we have set up works".
"Not a single Syrian refugee has been returned from Turkey unless it is of their free will," the Turkish prime minister said.
Meanwhile, Ms Merkel called for the establishment of special security zones on the Syrian side of the border, where refugees could find shelter.
"The more secure people can feel the less likely it is that they'll have to leave their homeland. So this is why we attach great importance to that," she said.
During the visit to the Nizip migrant camp, the EU officials met children and inspected living conditions. The camp is home to about 5,000 people.
Human rights groups criticised the visit as "sanitised".
Judith Sunderland, of Human Rights Watch, said the delegation should instead visit camps for the displaced on the other side of the border "to see the tens of thousands of war-weary Syrian refugees blocked" by Turkey from entering.
Under the EU-Turkey agreement, migrants who have arrived illegally in Greece since 20 March are to be sent back to Turkey if they do not apply for asylum or if their claim is rejected.
For each Syrian migrant returned to Turkey, the EU is to take in another Syrian who has made a legitimate request.
Opponents question its legality and argue that Turkey is not a safe place to return people to.
The scheme has reduced sharply the number of arrivals, from more than 56,000 in February to around 7,800 over the past 30 days, according to the European Commission.
However, the International Organization of Migration said unofficial data suggested numbers were picking up again.
Turkey already hosts some 2.7 million Syrian refugees, at a cost of over $10bn (£7bn), the government says.
Mrs Merkel's trip comes as she faces additional pressure for agreeing to the prosecution of German comedian Jan Boehmermann, who is accused of insulting Turkish President Recep Tayyip Erdogan by reading out a satirical poem.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.