Voting began at 8 a.m. (0500 GMT) and will end at 5 p.m. (1400 GMT).
Erdogan, 64, is seeking re-election for a five-year term with hugely increased powers under the new system, which he insists will bring prosperity and stability to Turkey, especially after a failed coup attempt in 2016 that has left the country under a state of emergency. If a candidate wins just over 50 percent of the vote, he will win the presidency, but if not, there will be a runoff on July 8.
There are six presidential candidates: Meral Aksener (Iyi "Good" Party), Selahattin Demirtas (Peoples" Democratic Party - HDP), Erdogan (Justice and Development Party - AKP), Muharrem Ince (Republican People's Party - CHP), Temel Karamollaoglu (Saadet "Felicity" Party) and Dogu Perincek (Vatan "Patriotic' Party).
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Turkish President Recep Tayyip Erdogan has said he expects the level of development of his country to reach the levels of Russian Federation and the United States.
It's the first time they'll be voting for president and parliament at the same time - a change approved past year by a referendum that switched Turkey's governance system to an executive presidency.
The men agreed that their children were too young to "truly remember" the bad days before Mr Erdogan, which is why the younger generation are supporters of the Kurdish HDP.
More than 56 million Turkish citizens are eligible to vote.
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The rallies and campaign vans have fallen silent, along with broadcast electioneering, hours before Turkey's polls are due to open.
Turkish President Tayyip Erdogan, accompanied by his grandchildren, casts his ballot at a polling station in Istanbul, Turkey June 24, 2018.
Ince further stressed that he would lift Turkey's state of emergency which has been in place over the past two years.
Erdogan blamed the coup on his former ally, USA -based Muslim cleric Fethullah Gulen, and has waged a sweeping crackdown on the preacher's followers in Turkey. According to the latest United Nations figures, some 160,000 people have been detained and almost as many more sacked in the crackdown.
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The president's critics, including the European Union which Turkey still nominally aspires to join, say Erdogan has used the crackdown to stifle dissent. "Backing the HDP means supporting democracy", Demirtas said in a video clip from prison, where he is being held on terror-related charges. A party must receive 10 percent of the votes for any of its candidates to win a seat at the legislature.