The referendum "is planned to take place on April 16," deputy prime minister Numan Kurtulmus said in comments broadcast on state-run TRT television.
Parliament in January approved a new 18-article constitution to create an executive presidency along the lines of that in the United States and France.
The government says the changes, which will scrap the office of prime minister, will ensure more effective leadership, but critics fear they would open the way for one-man rule.
The post of prime minister will be replaced with one or more vice presidents.
The parliamentary debate on the changes prompted violent scuffles, with the assembly witnessing fractious fighting.
The bill would allow for parliamentary and presidential elections to be held at the same time, with the draft giving November 3, 2019 as the date of the next ballot.
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