Turkey's president Recep Tayyip Erdogan has warned opponents not to "belittle" his narrow victory in a referendum that will grant him sweeping new powers.
Shortly afterwards, the main opposition party demanded the cancellation of the result, saying the referendum had been won through "illegal acts".
Their accusations appeared to have the backing of independent observers, who said the vote took place on an "unlevel playing field" and fell short of international standards.
But speaking to reporters in Istanbul, Mr Erdogan said results showed a winning margin of 1.3 million votes in what he described as a "historic decision".
Striking a conciliatory tone following the bitter contest, Mr Erdogan called on foreign powers to respect the outcome - which will mean 18 constitutional changes - as he thanked the Turkish people.
He said: "April 16 is the victory of all who said yes or no, of the whole 80 million, of the whole of Turkey of 780,000 square kilometres.
"We would like other countries and institutions to show respect to the decision of the nation."
But as he addressed thousands of flag-waving supporters in Istanbul a short time later, he was more defiant.
"There are those who are belittling the result. They shouldn't try, it will be in vain," he said.
"It's too late now."
The head of the country's electoral board confirmed the win shortly after Mr Erdogan spoke and said the final results would be known in 11-12 days.
The "yes" vote means Turkey's parliamentary system of government will be replaced with a presidential one and could see Mr Erdogan remain in office until 2029.
The office of prime minister is also set to be abolished, allowing the president to draft the budget, declare a state of emergency and issue decrees overseeing ministries without parliamentary approval.
The changes are due to come in after the next election, scheduled for 2019.
Opinion polls had shown a narrow lead for a "yes" vote before Sunday's ballot, but the country's three largest cities - Istanbul, Ankara and Izmir - and the mainly Kurdish southeast looked set to vote "no".
The referendum has bitterly divided Turkey and will affect the country's strained relations with the European Union.
President 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.
But critics say the move grants sweeping powers to Mr Erdogan following a failed coup last July.
A statement on the electoral board's website hours before polls closed said it would count ballots that had not been stamped by officials as valid, unless they could be proved fraudulent.
That triggered strong criticism from the main opposition People's Republican Party (CHP), which said the decision caused a serious legitimacy problem in the referendum.
Bulent Tezcan, the deputy chairman, said there was "only one way to to end the discussions about the vote's legitimacy and to put people at ease, and that is for the electoral board to cancel the vote."
The CHP vowed to challenge 37% of the ballot boxes, claiming on its Twitter account that data "indicates a manipulation in the range of 3 to 4%".
The country's pro-Kurdish opposition party added it planned to object to two-thirds of the ballots.
Residents in neighbourhoods in Istanbul banged pots and pans from their windows in protest at the result.
Turkey's prime minister, Binali Yildirim, declared victory for the "yes" campaign, and added: "In our democracy's history, a new page has opened."
Around 55 million people were eligible to vote in the referendum.