The Head of the Turkish Electoral Board said unofficial results show 1.25 million votes between yes and no.
It received many complaints that the voters were given envelopes without stamps from officials, the board said in a written statement while people were casting their votes on Sunday.
Here's everything you need to know.
SREENIVASAN: Was Turkey and was Erdogan conscious of what the rest of the world thought about this referendum and what happens tomorrow?
The administration of Turkey's president, Recep Tayyip Erdogan, is claiming victory in today's referendum to expand the president's executive powers.
The referendum comes six months after a military coup failed to unseat President Recep Tayyip Erdogan on July 15th 2016. The executive powers with the presidential office will then include assigning ministers, vice presidents and high-level state officials, as well as half the members in the Constitutional Court of Turkey. With 99 percent of the vote counted, 51.37 percent voted in favor of the constitutional amendments, while the "no" vote stood at 48.63 percent, according to an unofficial count.
So, what could the result mean for Turkey exactly? "Turkey is a tough country to rule", said Kamran Bokhari, a senior fellow with the Center for Global Policy and analyst with Geopolitical Futures. Final results will be released in 11 to 12 days, said electoral commission chief Sadi Guven.
Some 55 million people are eligible to vote across 167,000 polling stations, with the results expected to be announced late on Sunday evening.
After he cast his vote near his home in Istanbul, Mr Erdogan was greeted by a crowd chanting his name.
But Turkey's two main opposition parties said they would challenge the results after alleged violations.
What's it been like in the run-up to the referendum?
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The opposition has questioned the legitimacy of the vote. In fact, Erdoğan has already been controlling Turkey with nearly no checks and balances since 2014, and he and his allies have already purged roughly 130,000 people from the government thanks to the state of emergency declared following last year's failed coup attempt.
SREENIVASAN: How much of a factor did the attempted coup play into this vote?
What are the opposition to Erdogan saying? Opposition parties claim a win for the Yes side was called before all ballots had been counted.
CHP deputy head Erdal Aksunger also accused Turkish state media of "manipulating" the voting results.
"Our data indicates a manipulation in the range of 3 to 4 percent", the party said on its Twitter account.
What has the reaction to Erdogan's win been like in Turkey so far? "A one-man system is like that", said Istanbul resident Husnu Yahsi, 61, who said he was voting "no".
"There are no losers of this referendum. Turkey won, the beloved people won".
Foreign Minister Mevlut Cavusoglu told a group of supporters in his hometown of Antalya on Sunday: "As of now, there is a truly new Turkey".
But many also fear that the new system will endanger democracy in Turkey - a key USA ally and North Atlantic Treaty Organisation member.
The vote came as Turkey has been buffeted by problems.
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