President Recep Tayyip Erdogan declared an early victory in Turkey
With 98 per cent of the votes counted many now fear Erdogan has been given permission to shape Parliament to his wishes.
According to the agency Yes stands at 51.49%.
The Head of the Turkish Electoral Board said unofficial results show 1.25 million votes between yes and no.
There are 600,000 votes yet to be counted.
The ruling AK Party began celebrating early, despite the tight race.
Earlier on Sunday the campaign was delivered a blow as Turkey's three biggest cities Istanbul, Ankara and Izmir voted against him.
Erdogan said he will discuss the death penalty with the Prime Minister.He said in a televised speech in Istanbul: “If it [a parliament bill] comes in front of me, I will approve it.
“But if there isn't support (from the opposition in parliament)… then what shall we do?
“Then we could have another referendum for that.”
Istanbul explosions: 38 killed, 155 wounded in twin blasts
Mon, December 12, 2016
Dec 10th: Two blasts – a car bomb and suicide bombing – have killed 38 people and wounded 155 outside a football stadium in Istanbul. Turkey said on Sunday that Kurdish militants may be responsible for this apparent coordinated attack on police.
Get Quotes on Home Insurance
1 of 10
Turkish special force police officers patrol streets after a car bomb exploded near the stadium of football club Besiktas in Istanbul on December 10, 2016.
A win for Erdogan will represent one of the most dramatic overhauls of the country’s democratic system since the republic was founded in 1923.
The yes vote will also mean Mr Erdogan can abolish the post of prime minister – a role he had in 2003.
Immediately after he believed he had secured enough to win, Mr Erdogan said: “With the people, we have realised the most important reform in our history.
“Turkey for the first time in its history has decided with the will of the parliament and its people on such an important change.”
The international community began warning Erdogan late on Sunday, he should be careful.
Council of Europe Secretary General Thorbjorn Jagland said in a statement: “The Turkish electorate has voted on the amendments to the Constitution.
“In view of the close result the Turkish leadership should consider the next steps carefully."
The Turkish leader publicly fell out with European leaders in Brussels when he insisted he would bring back the death penalty for anyone he believed was involved in the failed coup of July 2016.
President Erdogan said he is considering bringing back the death penalty
Teachers, police officers, journalists, soldiers and opposition politicians have been arrested and detained.
Prisons in Turkey are filled with people labelled 'coup supporters' – often without evidence.