Queues formed from early morning at tightly guarded polling stations, and turnout by midday was around 40 per cent, according to a diplomatic source.
Polls closed at 6:00 p.M.(local time), and the election commission was expected to give overall turnout figures later in the evening.
In Washington, US Secretary of State John Kerry said Iraqis had "courageously voted," sending "a powerful rebuke to the violent extremists who have tried to thwart the democratic process and sow discord in Iraq and throughout the region."
Maliki encouraged a large turnout and voiced confidence he would stay in power after voting at a VIP polling centre in the Rasheed Hotel in Baghdad's heavily fortified Green Zone.
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"Today is a big success, and even better than the last elections, even though there is no foreign soldier on Iraqi soil," he said.
Maliki called for a move away from national unity governments towards ones of political majority, confidently telling journalists: "Our victory is certain, but we are waiting to see the size of our victory."
Parties have held rallies and candidates have angrily debated on television, but their appeals have largely been made on sectarian, ethnic or tribal grounds rather than political and social issues.
Analysts had expressed fears much of the electorate would stay at home rather than risk being targeted by militants, who killed nearly 90 people over the two previous days.
And fresh attacks were launched soon after polls opened, killing 14 people and wounding dozens.
Among those killed were two election commission employes who died in bombings as they were being escorted by a military convoy in northern Iraq.