Some 43.5 million Turks were eligible to elect more than 93,000 representatives in local assemblies across the country's 81 provinces - including mayors, city councillors, provincial councillors and village elders - who will serve for a term of five years.
One man was killed and some 10 injured in separate incidents a few hours ahead of the opening of polling stations, the Anatolia news agency reported.
An AKP member was killed in a brawl with members of the social democratic People's Party (SHP), in the southeastern town of Siirt.
In Denizli, in the west of the country, a member of the AKP was alleged to have opened fire on the local party headquarters of the People's Republican Party (CHP), wounding some 10 of its members, Anatolia reported.
The alleged attackers and an accomplice were arrested.
Opinion polls have given the AKP, led by Prime Minister Recep Tayyip Erdogan, a headstart over its rivals. It was expected to win the country's two main cities, Istanbul and the capital Ankara.
Some 43.5 million Turks are
eligible to vote
Surveys have predicted it would obtain more than 50% of the vote overall, a rare achievement in a country where support is notoriously fractured.
The AKP won 34% of the vote in the November 2002 general election, just a year after it was founded.
The CHP, the only other party in parliament, was expected to come second with some 20% of the vote.
Turkey's main pro-Kurdish movement, the Democratic People's Party (DEHAP), which has joined forces with several left-wing parties under the SHP banner, was expected to retain control of many municipalities in the southeast of the country, a Kurdish-majority region.
Since coming to power 18 months ago, the AKP has capitalised on an improving economy and moves to widen democracy to bring the Muslim nation closer to the European Union.
The ruling AKP is keen on having
Turkey join the EU
And the party, which has its roots in a banned Islamist movement, has steered clear of challenging the secularist elite and the army on matters of religious conscience.
It has notably refused to call for the lifting of a ban on the wearing of headscarves by Muslim women at universities and in public offices for fear of igniting a backlash.
Led by the charismatic Erdogan, a former Islamist and Istanbul mayor who now advocates secularism, the party was expected to win comfortably in Istanbul and Ankara, the country's two largest cities, according to one survey.
Local administrations have a limited role in Turkey's centralised government system, but the AKP is soon expected to adopt legislation to strengthen their powers.
Candidates from 20 parties as well as independents were contesting Sunday's election.
Surveys forecast a decline in the popularity of the social democratic CHP, which has built its strategy on a belligerent defence of secularist values and on accusations that the AKP harbours a secret Islamist agenda.