However, in Turkey's three largest cities - Istanbul, Ankara and Izmir - a majority voted "no".
Turkey's electoral authority rejected appeals to annul the referendum granting President Tayyip Erdogan wide new powers, but the main opposition CHP party said it will maintain its legal challenge to a vote it has said was deeply flawed.
The main opposition Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP) had on Tuesday asked that the poll be scrapped over alleged violations.
To the dismay of opposition parties and "No" supporters, the YSK made a last-minute decision on Sunday to accept ballot documents in envelopes without an official stamp.
The sweeping constitutional changes approved in the vote create a presidential system that will grant Erdogan more power than any leader since modern Turkey's founder Mustafa Kemal Ataturk and his successor Ismet Inonu. Turkey's main opposition party has filed a formal req.
Speaking in Ankara earlier, Prime Minister Binali Yildirim said the issue of the election result was closed and warned against street protests.
Supporters of the "no" vote, (Hayir in Turkish) chant slogans during a protest against the referendum outcome, in Istanbul, Tuesday, April 18, 2017.
"Trump spoke today with President Recep Tayyip Erdogan of Turkey to congratulate him on his recent referendum victory", the White House stated.
"HDP, CHP and Vatan Party appeals regarding the April 16 referendum were discussed separately and as a result of evaluations, the appeals were rejected with 10 votes against and 1 vote in favour", the electoral board said. "The opposition should not call people to take to the streets and say they do not recognize election results".
But the tight result of a highly charged campaign laid bare divisions, while European observers and the head of Turkey's bar associations union said a decision to count unstamped votes broke electoral law. "We will demand the rights of the voters until the end", he said.
A prosecutor will now consider whether to press charges against Guven.
The mission of observers from the 47-member Council of Europe, the continent's leading human rights body, said the referendum was an uneven contest. "From the German government's point of view, Turkey must. clear up the questions that have been raised".
Anadolu news agency cited a statement by Istanbul Police that said the suspects were detained early Wednesday for attempting to provoke a response similar to the mass anti-government demonstrations that happened across Turkey in 2013.
Erdogan has dismissed the criticism from the observers, telling the monitors to "know your place".
Turkish Foreign Minister Mevlet Cavusoglu on Wednesday accused the OSCE of bias and deliberately putting errors into its report.