Delivering a speech at the ruling Justice and Development Party (AKP) headquarters in Ankara after the referendum results, Turkey's prime minister thanked all voters. "It's good that election campaign, which was fought so bitterly, including here in Germany, is now over", Gabriel had said.
It is illegal to count the unstamped ballots as valid, Tezcan said.
In some affluent neighborhoods 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 may decide to turn inward, or turn away from the West and look for new allies in the east.
The High Electoral Board in Turkey made a late decision on the night of the referendum to count ballots that had not been stamped by officials, which observers said undermined important safeguards against fraud.
The 18 constitutional amendments that will come into effect after the next election, scheduled for 2019, will abolish the office of the prime minister and hand sweeping executive powers to the president.
The Council of Europe, a human rights organization which promotes European values and of which Turkey is a member, said the tight vote meant the country would have to proceed with caution.
A supporter of the "yes" brandishes a picture of Turkish president Recep Tayyip Erdogan.
The party has said it will contest the result of the referendum.
The glaring political problem in Turkey's southeast has been exposed once again even though the region has been largely pacified in military terms.
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But the main opposition party rejected the result and called for the vote to be annulled. Thousands of people marched through neighbourhoods of Istanbul, some chanting "Thief, Erdogan", "no to the presidency" and "this is just the beginning".
Erdogan's steady path toward authoritarian rule was bolstered by the Sunday election that drew 80 percent of eligible voters. Without them, it risks shrinking into a party of conservative provinces in Turkey's interior with only a few cities, notably the large cities of central Anatolia, as its strongholds.
His victory leaves the nation deeply divided and facing increasing tension with former allies overseas, while worldwide monitors and opposition parties have reported numerous voting irregularities. The rightists are divided.
Erdogan and the AK Party enjoyed a disproportionate share of media coverage in the buildup to the vote while the leaders of the pro-Kurdish People's Democratic Party (HDP), which opposes the changes, have been in jail for months.
Opposition parties called foul, complaining of a series of irregularities. And, unlike western political parties, it lives off generous budget subsidies rather than an active nationwide grassroots organisation.
CHP leader Kemal Kilicdaroglu said: "We respect the nation's will but the decision on unsealed ballots overshadowed it".
He also said he will approve the reinstatement of the death penalty if lawmakers submit a bill, or if Turkey holds a referendum to bring it back. The challenge has already been taken up by Brussels. "We are awaiting the assessment of the OSCE/ODIHR International Observation Mission, also with regard to alleged irregularities", a statement issued by EU President Jean-Claude Juncker and other ranking officials said.
Global observers from the Council of Europe and the Organization for Security and Cooperation in Europe (OSCE) are due to give their preliminary findings on the referendum later Monday. "But this time we will be moving slower and more calmly because of the experience we gained during and after the (Gezi) protests".
Ahmet Kasim Han, an associate professor at Kadir Has University in Istanbul, said the result would "profoundly change the way the country is governed".