Indonesian presidential candidate and current President Susilo Bambang Yudhoyono shows his ink-stained finger after casting his ballot with his wife, Kristiani Herawati, at a polling station in Cibubur, on the outskirt of Jakarta. (Achmad Ibrahim/Associated Press)

Polling stations have closed Indonesia's presidential election, with exit polls suggesting incumbent Susilo Bambang Yudhoyono has a clear lead.

Voting across the world's most populous Muslim country reportedly went off without violence or major controversy. More than 176 million people were eligible to vote in the nation's second direct presidential election.

Early exit polls suggest Yudhoyono has a comfortable lead and will likely take the election with about 59 per cent of the vote. He needs 50 per cent of ballots cast to win in one round.

Megawati Sukarnoputri, a former president whose father was the first postcolonial leader of Indonesia, was second at 28 per cent, with Vice-President Jusuf Kalla at 13 per cent.

Yudhoyono's opponents rejected the preliminary results and said they would wait for their own counts before responding.

An official result is to be released by the National Election Commission by July 27.

Yudhoyono has been praised for delivering peace to the restive province of Aceh and maintaining economic stablility in the face of the global financial crisis. The economy has been growing at four per cent a year.

Yudhoyono has also been credited with cracking down on the Jemaah Islamiyah terrorist network blamed for a series of attacks between 2002 and 2005 that killed more than 240 people, most of them foreign tourists on Bali.

Before dictator Suharto was ousted in 1998, Indonesia was under authoritarian rule for three decades.

Observers say Indonesia still faces severe corruption. It is also trying to attract foreign investment to improve its crumbling infrastructure, create an independent judiciary, and reduce the poverty of up to 100 million people.

With files from The Associated Press