Syrian refugees are seen at a tent camp on the outskirts of Izmir on April 28, 2016, in Izmir, Turkey. For many Syrian refugees, living in Turkey has become their only option. chris mcgrath/getty images

European Council President Donald Tusk said Tuesday that Ankara should not seek to change the rules agreed upon in the controversial EU-Turkey deal. Tusk's comments came as doubts lingered over the deal after Ankara threatened to walk out of negotiations if the EU did not ease travel rules for its citizens.

"The EU stands ready to fulfil its part of EU-Turkey deal as long as Turkey agrees to play by the rules, and not with the rules," Tusk said on Twitter.

Brussels wanted Ankara to narrow its definition of terrorism crimes as one of 72 requirements for visa liberalization, but Turkey refused, saying the law is crucial in battling Kurdish and Islamic State group fighters.

Under the deal, Ankara is to take back all migrants and refugees who cross the Aegean to enter Greece illegally, including Syrians. In return, the EU will take in thousands of Syrian refugees directly from Turkey and also provide money, visa-free travel and fast-track Turkey's progress toward EU membership. The deal caps the resettlement and return at 72,000 refugees, according to the EU's existing commitments.

Despite being criticized by several human rights group, the deal helped sharply cut the number of refugees and migrants reaching European shores since it went ahead on March 20.