The "Yes" campaign won 63.2 per cent of the vote while the "No" campaign mustered 36.8 per cent, the election commission said in figures quoted by the NTV channel, in an initial count based on 25 per cent of the ballot boxes. But according to the state-run Anadolu Agency, with 100 percent of the ballots counted, Erdogan appeared poised to win with 51.2 percent of voters casting ballots in his favor.
Turnout across the country was 87 percent.
Prime Minister Binali Yildirim, who leads the ruling Justice and Development Party, was nominated to lead the government in May after Ahmet Davutoglu stepped down amid differences with Erdogan. Other opposition players echoed the assertion, with the Peoples' Democratic Party claiming on Twitter that its "data indicates a manipulation in the range of 3 to 4 percent". Term limits for the president would be changed and Erdogan would be allowed to remain in power until 2029. Voters use an official stamp to select between "yes" and "no" - the question itself is assumed to have been understood by all in advance.
People were already lined up at an Istanbul polling station before it opened.
The new constitutional system will get rid of the role of prime minister and transform the presidency from a largely ceremonial position into a vastly powerful post as both head of state and head of the government. The changes would come into effect with the next general elections, scheduled for 2019.
Istanbul resident Husnu Yahsi, 61, also said he was voting "no".
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But Mr Tillerson repeated the administration's new belief that "the reign of the Assad family is coming to an end". Putin also asserted that Syria has complied with an agreement to dispose of chemical weapons "so far as we know".
"We are voting for Turkey's destiny", said the standard- bearer of the "No" camp, Republican People's Party (CHP) leader Kemal Kilicdaroglu. "He's governing so well". The AP reports that supporters of the "yes" vote have dominated the airwaves, while supporters of the "no" vote have complained of intimidation.
Erdogan has painted supporters of the "no" campaign as people bent on destabilizing the nation, accusing them of siding with terrorists blamed for the July 2016 attempted coup.
Voters can vote Yes or No to an 18-article proposal to switch Turkey from a parliamentary to a presidential system.
Turkey has also suffered renewed violence between Kurdish militants and security forces in the country's volatile southeast, as well as a string of bombings, some attributed to the Islamic State group, which is active across the border in Syria. Some 100,000 people, including judges, lawyers, teachers, journalists and police, have been dismissed from their jobs. Hundreds of media outlets and nongovernmental organizations have been shut down. Turkey has sent troops into Syria to help opposition Syrian forces clear a border area from the threat posed by Islamic State militants.
Tensions flared between the governments of Turkey and European countries, particularly Germany and the Netherlands, over restrictions on Turkish politicians campaigning for the votes of compatriots who live overseas.