A defiant Turkish President Tayyip Erdogan has denounced the West's "crusader mentality" after European monitors criticised a referendum to grant him sweeping new powers, won with a narrow victory.

Addressing a crowd of flag-waving supporters from the steps of his palace in Ankara, Erdogan told election observers to "talk to the hand" and said it would not be so important to Turkey if the European Union broke off accession talks.

Sunday's vote ended all debate on forging a stronger presidency, Erdogan said. 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".

Election authorities said preliminary results showed 51.4 per cent of voters had backed the biggest overhaul of Turkish politics since the founding of the modern republic.

Erdogan says concentrating power in the hands of the president is vital to prevent instability. But the narrowness of his victory could have the opposite effect: adding to volatility in a country that has lately survived an attempted coup, attacks by Islamists, a Kurdish insurgency, civil unrest and war across its Syrian border.

The result laid bare the deep divide between the urban middle classes who see their future as part of a European mainstream, and the pious rural poor who favour Erdogan's strong hand.

Erdogan reiterated his readiness to restore the death penalty at several appearances on Monday, which would effectively end Turkey's decades-long quest to join the EU.

"The crusader mentality in the West and its servants at home have attacked us," he said.

"We neither see, hear, nor acknowledge the political reports you'll prepare.

"We'll continue on our path. Talk to the hand. This country has carried out the most democratic elections, not seen anywhere in the West."

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. Support for "Yes" dominated campaign coverage, and the arrests of journalists and closure of media outlets silenced other views, the monitors said.

"In general, the referendum did not live up to Council of Europe standards. The legal framework was inadequate for the holding of a genuinely democratic process," said Cezar Florin Preda, head of the delegation.

A last-minute decision by electoral authorities to allow unstamped ballots to be counted undermined an important safeguard and contradicted electoral law, they said.

Critics accuse Erdogan of steering Turkey towards one-man rule. The two largest opposition parties both challenged Sunday's referendum, saying it was deeply flawed.

The president survived a coup attempt last year and responded with a crackdown, jailing 47,000 people and sacking or suspending more than 120,000 from government jobs such as schoolteachers, soldiers, police, judges or other professionals.

The changes could keep him in power until 2029 or beyond.

Under the changes, most of which will only come into effect after the next elections due in 2019, the president will appoint the cabinet and an undefined number of vice-presidents, and be able to select and remove senior civil servants without parliamentary approval.