Turkey's President Recep Tayyip Erdogan has claimed victory in a referendum granting him sweeping new powers, hailing the result as an "historic decision".

The leader called on the international community to respect the result and discouraged his critics from "belittling" the outcome, saying they "shouldn't try, it will be in vain".

The state-run Anadolu news agency claimed that 51 per cent per cent of voters had sided with the "Yes" campaign, ushering in the most radical change to the country's political system in modern times.

Turkey Referendum: Votes are cast in Ankara

But the main opposition the Republican People's Party (CHP) said they would demand a recount of up to 40 per cent of the vote, saying that "illegal acts" occurred during the vote and that there were up to 2.5m "problematic ballots". The pro-Kurdish People's Democratic Party (HDP) also claimed they had information that voter fraud was implicated in up to four per cent of the ballots. Both parties said they would appeal the results.

The Supreme Election Commission said it would make the unprecedented decision to count ballots that had not been stamped by its officials as valid unless they could be proved fraudulent, citing a high number of complaints that its officials at polling stations had failed to stamp them.

​Anadolu reported that Mr Erdogan had called allied political leaders to congratulate them over the yes win, with the words: “May this result be fortunate for our nation.” Meanwhile, Mr Erdogan was said to have told Prime Minister Binali Yildirim that the results were “clear”, according to presidential sources.

As Mr Erdogan's supporters celebrated on the streets of Istanbul with fireworks, the CHP said that “illegal acts” were carried out in favour of the government in the referendum.

Referring to the decision to count ballots without validation stamps, CHP Chairman Kemal Kilicdaroglu said: “You cannot change the rules of the game in the middle of the game," adding that the board had “cast a shadow on the results”.

Yet the head of Turkey’s high electoral board Sadi Güven refuted the claims, saying the decision to count votes without stamps was taken before the results were entered into the system and that members of the AKP and the main opposition were present at almost all polling stations and signed off on reports.

He also confirmed that the “Yes” campaign had won based on unofficial results. With only about 600,000 votes still to be counted, 1.25m Turkish voters had opted to expand the President’s powers, Mr Güven told reporters in Ankara. He added that official results were expected in 11-12 days

The leader of Turkey's nationalist MHP opposition party, Devlet Bahceli – who supported the "Yes" campaign – said that the outcome of a referendum on boosting the powers of Mr Erdogan was an “undeniably successful achievement” and should be respected.

Speaking to reporters in Istanbul, Mr Erdogan said unofficial results showed the “yes” side had won by a margin of 1.3 million votes.

The President struck a conciliatory tone, thanking all voters regardless of how they cast their ballots and describing the referendum as an “historic decision”.

“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 kilometers,” he said.

Turkey's foreign minister said the win brought about the birth of a “new Turkey”. Foreign Minister Mevlut Cavusoglu told a group of supporters in his hometown of Antalya on Sunday: “As of now, there is a truly new Turkey. There will be stability and trust in the new Turkey.”

But, with the opposition parties stating that a re-count was required, it may be some time before a definitive result is reached. The HDP claimed that results would not be final until their appeal had been heard.

“The referendum result is a clear sign that a societal agreement could not be reach," HDP spokesman Osman Baydemir said. "Our co-chairs being jailed, the referendum being held under a state of emergency, and other oppressive measures cast a shadow and legitimacy problem over the vote,”

The vote introduces a raft of constitutional changes that mean Turkey's parliamentary democracy can be replaced with an executive presidency. Mr Erdogan said Turks could expect the process to be complete by November 2019.

After the constitutional changes come into effect, Mr Erdogan will have the ability to stay in power until at least 2029 — since he will gain the chance to run for re-election in 2019 and potentially serve two five-year terms.

The referendum result also allows him to re-take control of the ruling Justice and Development party (AKP) that he helped to found. Mr Erdogan spent 11 years as Turkey's Prime Minister, and head of the AKP, before becoming the country's first directly-elected President in August 2014 — a supposedly ceremonial role.

The vote has opened bitter political divides in Turkey. Before voting closed, Anadolu reported that two people died in a fight outside a polling station in the southeastern province of Diyarbakir.

Although the exact reason for the dispute was not known, Dogan news agency reported it as caused by "differences in political opinion".

Anadolu news agency said a quarrel between two families turned deadly Sunday in a village school's garden where people were casting their votes on Turkey's referendum.

The “Yes” campaign says the changes would streamline Turkey’s political system, and pointed out that both the US and France have an executive presidency.

But opponents fear the concentration of the power in the office of the Presidency would cause the country to lurch further towards authoritarianism and one-man rule.

Shortly after state media announced the result, Mr Erdogan said he would "take up" the issue of reinstating the death penalty in Turkey, a long-sought objective of his.

The outcome will also shape the republic's strained relations with the European Union. Turkey, a Nato member state, has curbed the flow of refugees and migrants – mainly refugees from wars in Syria and Iraq – using a route from Turkey to enter the bloc, but Mr Erdogan says he may review the deal after the vote.

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Turnout for the vote was 86 per cent, the President claimed. According to vote-tracking by Anadolu, the "Yes" campaign took a strong lead early in the early stages of counting, holding nearly 60 per cent of the vote after 38 per cent of ballots had been tallied.

Yet that lead narrowed when results came in from outside areas where there was strong support for Mr Erdogan.

The news agency showed a high percentage of "Yes" votes in central Anatolia, a traditional stronghold for the AKP politician, while "No" votes led in coastal regions near the Aegean Sea and Turkey's mainly Kurdish southeast.

In Turkey's three biggest cities – Istanbul, Izmir and the capital Ankara – the “No” camp appeared set to prevail narrowly, according to Turkish television stations.

After he cast his vote near his home in Istanbul, Mr Erdogan was greeted by a crowd chanting his name. His staff handed out toys for children in the crowd.