The polls are being seen as a key test for PM Recep Tayyip Erdogan ahead of presidential elections in August and parliamentary elections in 2015.
It is the first vote since mass protests last June, and subsequent government corruption scandals.
Recep Tayyip Erdogan is not standing but has campaigned tirelessly in support of his Justice and Development Party (AKP).
With about a half of the votes counted, Recep Tayyip Erdogan’s party was leading the main opposition party 45% to 27%.
The AKP had been aiming to equal or better its 38.8% share of the vote in 2009.
Voting in the local assembly and mayoral elections passed off peacefully in most areas, but eight people were reportedly killed in two separate incidents involving supporters of rival candidates.
Feuding families were said to have clashed in the southern city of Hatay and the eastern province of Sanliurfa.
Recep Tayyip Erdogan has been eyeing a run for the presidency in August – the first time voters will directly elect the head of state – or may seek to change the rules to allow him to seek a fourth term in office.
In the run-up to Sunday’s poll, the government blocked Twitter and YouTube, following a series of online leaks.
Recep Tayyip Erdogan said social media was spreading misinformation.
On Saturday pro- and anti-government factions held rival demonstrations in Istanbul, which saw the Gezi Park protests of May and June last year.
The secular opposition Republican People’s Party (CHP) is fighting to win the Istanbul mayor’s office from Recep Tayyip Erdogan’s ally Kadir Topbas. However, early results put the AKP ahead in the sprawling metropolis.
Recep Tayyip Erdogan is a former mayor of Istanbul and the vote has become an unofficial referendum on his administration. The prime minister himself has described the vote as a struggle for Turkey’s independence.
The race looked tighter in the capital Ankara, with the AKP narrowly leading the CHP.
The loss of either city would be a major embarrassment for the prime minister.
More than 50 million people are eligible to vote, and turnout appeared to be high.
Recep Tayyip Erdogan has purged hundreds of people from the judiciary and police since several of his allies were arrested over a corruption scandal in December.
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