Updated 9.45pm - Turkish President Tayyip Erdogan claimed victory in Sunday's presidential election and said his ruling AK Party and its alliance partner had won a parliamentary majority.

However, the main opposition party said it was too early to concede defeat and said it believed Erdogan could still fall short of the 50 percent needed to avoid a runoff on July 8.

"Our people have given us the job of carrying out the presidential and executive posts," he said in a short speech from Istanbul.

"I hope nobody will try to cast a shadow on the results and harm democracy in order to hide their own failure."

Sunday's vote ushers in a powerful new executive presidency long sought by Erdogan and backed by a small majority of Turks in a 2017 referendum. Critics say it will further erode democracy in the NATO member state and entrench one-man rule.

An unexpectedly strong showing by the AK Party's alliance partner, the nationalist MHP, could translate into a stable parliamentary majority Erdogan seeks to govern freely.

In early trading in Asia the lira currency firmed modestly against the dollar on the prospect of increased political stability.

Erdogan's main presidential rival, Muharrem Ince of the main opposition Republican People's Party (CHP) urged election monitors to remain at polling stations to help ensure against possible election fraud, as final results came in from large cities where his party typically performs strongly.

With 96 percent of votes counted in the presidential race, Erdogan had 53 percent, comfortably ahead of Ince on 31 percent, broadcasters said.

In the parliamentary contest, the Islamist-rooted AK Party had 43 percent and its MHP ally 11 percent, based on 98 percent of votes counted, broadcasters said.

In the opposition camp, the CHP had 23 percent and the pro-Kurdish Peoples' Democratic Party (HDP) 11 percent - above the threshold it needs to reach to enter parliament.

The HDP's presidential candidate, Selahattin Demirtas, has waged his election campaign from a prison near the Greek border as he awaits trial on terrorism-related charges, which he denies. He had 7 percent, based on 90 percent of votes cast.

The opposition raised doubts about the accuracy and reliability of the figures released by state-run Anadolu news agency, the sole distributor of the official vote tally. 

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