Queues formed from early Wednesday morning at tightly-guarded polling stations despite a surge of violence before the elections targeting campaign gatherings and early voting by security personnel.
Maliki encouraged voters to turn out in large numbers and voiced confidence he would stay in power after casting his ballot at a VIP polling center in the Rasheed Hotel in Baghdad's heavily-fortified Green Zone.
"Today is a big success, and even better than the last elections, even though there is no foreign soldier on Iraqi soil," the premier said.
He called for a move away from national unity governments towards ones of political majority, and confidently told journalists: "Our victory is certain, but we are waiting to see the size of our victory."
The run-up to the election, the first parliamentary poll since US forces departed in December 2011, has seen Baghdad and other major cities swamped in posters and bunting.
Parties have staged rallies and candidates have angrily debated on television, though appeals to voters 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.
Fresh attacks were launched soon after polls opened on Wednesday morning, killing 14 people and wounding dozens more.
Security officials reported more than 50 mortars, roadside bombs and suicide attacks in all, mostly targeting polling stations or people on their way to vote in northern and western Iraq.
Among those killed were two employees of Iraq's electoral commission who died in two bomb blasts as they were being escorted by a military convoy in northern Iraq.
Also north of Baghdad, militants seized a polling station and blew it up, after expelling election staff and those waiting to vote.
But many Iraqis said they were determined to vote despite the unrest, voicing disdain for the current crop of elected officials. Others voiced confidence in Maliki and his Shia-led government.
More than 750 people have been killed this month alone, as violence hit its highest levels since a brutal sectarian conflict killed tens of thousands in 2006 and 2007.
Militants have controlled the town of Fallujah since the beginning of the year, preventing polling from being held in parts of mainly Sunni Arab al-Anbar province, west of Baghdad.
Maliki's critics have accused him of concentrating power and marginalizing the Sunni minority, and say public services have not sufficiently improved during his eight-year rule.
The 63-year-old contends the violence is fuelled by the civil war in neighboring Syria and has accused Saudi Arabia and Qatar of backing insurgents.
Maliki's State of Law alliance is tipped to win the most seats in parliament but fall short of a majority, meaning he will have to court other Shia parties, as well as Sunni and Kurdish blocs, if he is to remain in power.
Although Maliki faces significant criticism, analysts say a fractious and divided opposition leaves him the frontrunner for the top job.
HH/HH