The main opposition Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP) said they would challenge the results from most of the ballot boxes due to alleged violations.
Mr Erdogan has insisted the changes are needed to amend the current constitution, which was written by generals following a 1980 military coup, to confront security and political challenges in Turkey and avoid past fragile coalition governments.
In his first remarks from Istanbul after the vote count showed the amendments winning approval, Erdogan struck a conciliatory tone, thanking all voters no matter how they cast their ballots and calling the referendum a "historic decision".
He also said an unprecedented decision by the country's electoral board to accept as valid ballots that didn't bear the official stamp was taken following a complaint by an official from the governing party.
Three people were killed in a shootout in the garden of a school used as a polling station in the southeastern Diyarbakir region, the Dogan news agency said, but it was not clear if the fighting was linked to the election or simply a family feud.
In some affluent neighbourhoods in Istanbul, people took to the streets in protest while others banged pots and pans at home - a sign of dissent that was widespread during anti-Erdogan protests in 2013.
Turkey's President Recep Tayyip Erdogan waves to supporters in Istanbul, Turkey, on Sunday, April 16, 2017.
California Gas Tax 2017: Governor Jerry Brown Expected To Sign SB1 Bill
Janet Nguyen (R-Garden Grove) spoke of the hardships the tax and fee increases will impose on poor and middle-class Californians. The base excise tax will jump 12 cents per gallon for regular gasoline and 20 cents per gallon for diesel fuel.
As of 11.30 p.m. local time (2030GMT), unofficial results showed Yes won with 51.37 percent - 24,966,843 votes - while No had 48.63 percent, or 23,636,067 votes.
Turnout across the country was 85.46 percent. However, Deputy Prime Minister Mehmet Simsek told Reuters there was no such plan, and the elections would still be held in 2019. "The German government ... respects the right of Turkish citizens to decide on their own constitutional order", the chancellor, Angela Merkel, and her foreign minister said.
Erdogan has been consolidating power for years and eliminating opposition rivals, but the European part of the country is resoundingly voting against the constitutional changes.
Critics say the move was created to shut down the opposition, with more than 40,000 arrests and an estimated 100,000 people removed from their government posts.
Erdogan argued the changes would guarantee stability in Turkey - a message that resonates in a country that's suffered a spate of suicide bombings, as well as an attempted military coup last July that almost ousted the president from power.
Turkey has shown itself more polarised than ever tonight.
Opposing parties said that this referendum is a step towards additional tyranny in a country where more than 47,000 were imprisoned and more than 140,000 were dismissed during a campaign post the failed coup in July, leading to criticizing Turkey by its allies in the West and the global rights organization.
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