Yesterday's referendum greatly expands the powers of Erdogan's office, and could see him reign until the year 2029.
State-run Anadolu news agency said votes in favour of allowing 18 constitutional changes stood at 51.3% with 98% of ballots counted.
Immediately, Erdogan proclaimed victory; however, the narrow margin has encouraged the opposition to say it would demand a recount of about 37% of the ballet boxes, containing around 2.5 million votes. Opponents fear the changes will lead to autocratic one-man rule under Erdogan.
Polls in the east opened at 7 a.m. (0400 GMT), while those in the west are to open an hour later.
"Turkey for the first time in its history has decided with the will of the parliament and its people on such an important change", he said. "He's governing so well", Mualla Sengul said.
Prime Minister Binali Yıldırım also delivered a speech toward the end of the vote count and pledged that his Justice and Development Party (AK Parti) government would respect both "Yes" and "No" votes. The president will become the head of the executive branch and will be allowed to issue decrees, including the right to declare a state of emergency.
He also noted that not all articles of the reforms will go into effect immediately and some of them will remain until November 2019.
The president will have a five-year tenure, for a maximum of two terms.
But the first signs suggested that yet another ballot box win had only emboldened the "chief", as he called on foreign powers to respect the result and mooted a referendum on restoring the death penalty - which would sound the death knell for Turkey's European Union bid.
A controversial proposal to extend the powers of the Turkish President Recep Tayyip Erdoğan has been rejected by with an overwhelming majority of the Turkish expatriates in Switzerland.
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The officials weren't authorized to speak publicly on the results of the policy review and requested anonymity. After South Korea, Pence is scheduled to travel to Japan, Indonesia and Australia during his 10-day trip.
The referendum campaign was highly divisive and heavily one-sided, with the "yes" side dominating the airwaves and billboards.
The vote came as Turkey has been buffeted by problems. Supporters of the "no" vote complained of intimidation, including beatings, detentions and threats.
They also argue that the current constitution, written by the generals who ruled Turkey in the years following a 1980 coup, still bears the stamp of its military authors and, despite numerous revisions, must be overhauled.
Western countries have criticized that tough response, and relations with the EU - which Turkey has been negotiating to join for a decade - hit a low during the campaign when Erdogan accused European leaders of acting like Nazis for banning referendum rallies in their countries on security grounds.
His election campaigns have been forceful and bitter, with Erdogan lashing out at his opponents, accusing them of endangering the country and even supporting terrorism.
Roughly 100,000 people, including judges, teachers, academics, doctors, journalists and members of the military and police forces, have lost their jobs, and more than 40,000 have been arrested.
Hundreds of non-governmental organizations and news outlets have been shut down, as have many businesses, from schools to fertility clinics.
The new system, he argues, will resemble those in France and the U.S. and will bring calm in a time of turmoil marked by a Kurdish insurgency, Islamist militancy and conflict in neighbouring Syria, which has led to a huge refugee influx.
The war in Syria has led to some 3 million refugees crossing the border into Turkey.
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