Turkey's EU Affairs Minister Omer Celik said on Tuesday the European Union should implement visa-free travel for Turkish citizens by the end of year and stop insisting that Ankara change its anti-terrorism laws.
He warned Turkey may cancel its side of a deal to readmit illegal migrants if the EU does not keep the promises it made.
Turkey agreed in March to stop illegal migrants from crossing into Greece in exchange for financial aid for those in its care, the promise of visa-free travel for its citizens to much of the EU, and accelerated EU membership talks.
But there has been deadlock over the plan to grant Turkish citizens visa-free access to Europe by October.
Brussels first wants Turkey to change its anti-terrorism laws, which it deems too broad and potentially oppressive for European standards.
In an interview with Reuters, the minister said that, "Forcing this despite the situation is putting a roadblock in front of the visa liberalisation, and therefore we will assume they aren't keeping the promises they made."
"In that case we won't carry out the readmission deal, and we will cancel it if necessary," he said, referring to the 2013 deal in which Turkey agreed to take back migrants who travelled illegally to the EU in return for the promise of visa-free travel.
He said no final demand for a schedule had yet been given by Turkey, but that if visa liberalisation is not implemented by the end of the year it would have "reached its natural death".
"There won't be anything left to talk about," he added.
More than a million migrants entered the EU last year by boats from Turkey to Greece, but the numbers taking that route have tumbled since the deal with Ankara came into effect.
Celik said Turkey had been keeping its promises, with illegal arrivals on the Greek islands dropping to 20-30 people a day from a peak of 7,000 in 2015.
"If there is a working part of the deal, it is because of the working quality of Turkish institutions. It is thanks to the security forces and coast guard," he said.
"There is nothing holding the deal back in terms of Turkey realising its promises, but every aspect is lagging from the European side."
The EU said this month it was living up to its side of the agreement, and that financial support for migrants in Turkey had accelerated in recent months.