"I hope that the visa exemption... Will constitute a positive step in fulfilling the promises made and speed up the accession process," Erdogan said in a statement, reaffirming EU membership as a "strategic goal" for Ankara.
Erdogan's message, marking Europe Day, came after he warned Brussels Friday that Turkey would not modify an anti-terror law for the sake of the deal with the bloc on visa-free travel.
Turkey struck a deal with the EU in March to curb the flow of migrants into Europe in exchange for a range of incentives, including easing visa requirements for Turks.
According to the plan, Turks will benefit from the new travel rules by June and the European Commission has already given its recommendation for this to go ahead.
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But Prime Minister Ahmet Davutoglu - who brokered the migrant deal with the EU - announced last week he was stepping down, rasing fears the president could impose obstacles in front of the accord.
In a blunt message to the EU on Friday, Erdogan said: "The EU says: you will change the anti-terror law for visas ... Pardon me but we are going our way and you can go yours."
He vowed Turkey would continue to cooperate with the EU on a series of issues and added: "We hope Europe will not be a region where tough migrant policies as well as discrimination, intolerance against migrants and Islamophobia are on the rise.