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7 year oldHe was speaking in Istanbul as the count neared completion. With more than 99% of ballots counted, "Yes" was on 51.36% and "No" on 48.64%.
Erdogan supporters say replacing the parliamentary system with an executive presidency will modernise the country.
The two main opposition parties are challenging the results.
As jubilant Erdogan supporters rallied in the big cities, pots and pans were banged in Istanbul by opponents of the referendum, in a traditional form of protest.
If confirmed, the "Yes" vote could also see Mr Erdogan remain in office until 2029.
Three people were shot dead near a polling station in the south-eastern province of Diyarbakir, reportedly during a dispute over how they were voting.
Erdogan's Turkey: The full story
Turkey referendum: Key reactions
Supporters are streaming into the governing AK party's headquarters here in Ankara, car horns and campaign songs blaring - they are convinced the "Yes" side has won and that President Erdogan now has a mandate for the biggest political reform in Turkey's modern history.
The president has claimed victory but the opposition disputes it, complaining of massive irregularities with the voting, suggesting the state news agency manipulated results and vowing to challenge them with the supreme election board.
Turkey has shown itself more polarised than ever tonight. And if the protests gather steam, this could get ugly.
Critics abroad fear Erdogan's reach
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