Mr Ince, a former teacher and the presidential candidate of the main opposition party, the secularist Republican People's Party (CHP), has proved highly effective on the campaign trail, drawing huge crowds, especially in the big cities. The streets, however, appear to be rather empty as of now.
The HDP passing the threshold is key for the opposition: Forecasts show that without them in parliament, the AKP and their junior coalition partner, the Nationalist Movement Party (MHP), would once again win the majority of seats.
The president's critics, including the European Union, which Turkey still nominally aspires to join, say Erdogan has used the crackdown to stifle dissent. Fatih Bayhan, a 55-year-old trader, came to his polling station at 5am to monitor the handling of ballots.
Ballots of Turkey's presidential and parliamentary elections are being counted at a polling station in Diyarbakir, Turkey June 24, 2018. Goran Tomasevic / Reuters 0922: What's at stake? Those attempting the fraud were claimed to be supporters of a parliamentary candidate from the ruling Justice and Development Party (AK Parti) list, whose name had also been involved in a clash in the same town 10 days ago in which four people were killed.
Mr Erdogan, 64, who has dominated Turkish politics for 15 years, first as prime minister and since 2014 as president, praised the executive presidency that comes into force after the election.
Initial results were expected later in the day.
The elections will complete Turkey's transition to a new executive presidential system, a move approved in a controversial referendum a year ago.
With more than 62 percent of the parliamentary votes counted, the AK Party's People's Alliance was ahead with 56.7 percent of the votes and the Nation's Alliance was in second place with 32.1 percent of the votes.
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Voting already closed last week for Turkish citizens resident overseas, with just under 1.5 million out of just over 3 million registered voters casting their ballot, a turnout of just under 49 percent.
Prominent pollster Gezici predicted that with 48 per cent of votes, Erdogan would just fall short of the 50 per cent mark needed to secure a first-round victory.
Erdogan, who held five rallies in Istanbul on June 23, called on supporters to be vigilant at the polling stations. Without them, many said, the country could not function.
"Turkey", he said, "is staging a democratic revolution".
The pro-Kurdish HDP has seen nine of its lawmakers and thousands of party members arrested by the government and says more than 350 of its election workers have been detained since April 28.
Turkey is no stranger to allegations of election rigging.
Selahattin Demirtas, the presidential candidate of the pro-Kurdish Peoples' Democratic Party, or HDP, was forced to run his campaign from prison, where he is being held in pre-trial detention on terrorism-related charges.
With the polls officially closed, electoral committees across the country's 81 provinces have started counting the ballots. "Here we hardly feel the state of emergency that's still ongoing".