(CNN) Iraqis voted Saturday in their first parliamentary elections since the defeat of ISIS last year, with the economy, jobs, security and corruption high on the list of voters' concerns as the country seeks to rebuild after years of conflict.

Nearly 7,000 candidates contested 329 seats in the parliament, of which a quarter must go to women . More than 24 million Iraqis registered to vote, according to Iraq's electoral commission, and more than 55,000 polling stations opened across the country.

According to an update from the Iraqi Electoral Commission on Iraqi state TV Al Iraqiya, 44% of eligible voters turned out for the election.

Polls closed at 6 p.m. local time. It could be days before the winners are announced.

"Our dear people have been able to freely and safely cast their votes to choose their representatives," Prime Minister Haider al-Abadi said in a statement after polls closed. "I salute our heroic forces, government agencies, state institutions, the media, and all those involved in the success of the electoral process."

However, four civilians were killed in an explosion on their way to vote in the Haweja area just west of Kirkuk on Saturday. A police official said the attack deliberately targeted civilians heading to the polling stations.

As a result, security officials implemented a curfew from midnight to 6 a.m. Sunday in the province of Kirkuk.

Shortly before the polls closed, State of Law Coalition, a rival party headed by former Prime Minister Nuri al-Maliki, expressed concern that "some political forces have resorted to the use of various types of threats and intimidations, and threats to use weapons against polling stations and voters in order to influence their choices and vote for the candidates of some who already are realizing their early defeat."

Under the power-sharing system installed after the 2003 US-led invasion, the position of prime minister is reserved for a Shiite.

Abadi, who's been in power since 2014, is hoping to win back the top job. But the country's Shiite bloc has splintered into five major coalitions, making it hard to predict which will come out on top.

Whoever wins will still need to reach out to other blocs, including Sunni and Kurdish coalitions, to form a governing alliance.

The next prime minister will then face the daunting task of stabilizing a nation scarred by ISIS' rise and still plagued by sectarian division at a critical juncture in its history.

Followers of Shiite cleric Muqtada al-Sadr carry a huge Iraqi flag as they take part in a campaign rally in Baghdad on May 4.

The US Secretary of State's office sent a congratulatory note to the Iraqi people, saying: "The United States stands ready to partner with Iraqi leaders as we continue to build a long-term relationship of cooperation and friendship between our two nations -- a strategic partnership based on the Strategic Framework Agreement that will contribute to stability in the region and growing peace and prosperity in Iraq."

Abadi credited with defeating ISIS

Abadi, who heads the Nasr, or Victory, coalition, is widely credited in Iraq with helping to reconstruct the Iraqi Army and defeat ISIS. He hoped to capitalize on that support even as many voters lamented a lack of improvement in their daily lives.

Ahead of the election, Abadi sought to broaden his coalition to bring in significant Sunni figures and avoid overt sectarianism -- and his was the only coalition running in all 18 of Iraq's provinces. He cast his vote Saturday in the Baghdad neighborhood where he was born.

During the war against ISIS, Abadi succeeded in balancing the interests of Iraq's powerful neighbor, Iran, and the United States, as well as significantly improving relations with Saudi Arabia and boosting Iraq's diplomatic standing overall.

Baghdad also regained control of disputed oil-rich fields in Kirkuk last year following a contentious Kurdish independence referendum in September . While that has not endeared Abadi to many Kurds, outside the Kurdish region he is credited with taking a strong position and reasserting central government control without major bloodshed.

But many Iraqis are also frustrated by the limited change they've seen in their daily lives.

Among their complaints are a dearth of job opportunities, a struggling economy and crumbling infrastructure, with frequent power cuts. They also lament poor government services and slow reconstruction in areas such as Tikrit, Falluja and Mosul that were devastated in the battle against ISIS.

Corruption, another major issue, is blamed by many Iraqis for their country's failure to translate the wealth from its natural resources into a better life for all its citizens.

Iraqi Prime Minister Haider al-Abadi talks during a campaign rally in the holy city of Najaf on May 3.

Chief rivals

Abadi's chief rivals included Maliki, who leads the State of Law coalition.

During his two terms in power, from 2006 to 2014, Maliki was widely seen as having alienated a large part of the Sunni population and by doing so having prepared the ground for the rise of ISIS. But he maintains significant support and has close ties to Iran.

Nuri al-Maliki speaks during a tribal gathering on May 13, 2017, in Najaf.

Another significant contender was Hadi al-Amiri, who heads the Fatah (Conquest) coalition and also has strong links with Tehran, having spent much of his youth in exile in Iran and fought on the side of the Iranians in the Iran-Iraq War.

Amiri helped command the Hashd al Shaabi, or Popular Mobilization Units (PMU) -- the largely Shiite, pro-Iranian paramilitary force that supported the Iraqi Army in the fight against ISIS.

Hadi al-Amiri, leader of the Fatah Alliance, a coalition of Iranian-supported militia groups, speaks during a campaign rally in Baghdad on May 7.

While the PMU played a vital role in defeating ISIS, some groups under its umbrella were accused of committing sectarian abuses against Sunnis and Kurds, an allegation the PMU denied.

Last week, Iraq's highest Shiite religious authority, Grand Ayatollah Ali al-Sistani, urged voters not to reelect "corrupt" lawmakers and warned that "foreign agendas" could undermine the country's ability to carry out a free and fair vote.

In a televised statement delivered by his representative after Friday prayers, al-Sistani urged voters to learn from the past. "Avoid falling into the trap of those who are corrupt and those who have failed, whether they have been tried or not," he said.

It was al-Sistani's call for Iraqis to take up arms against ISIS in 2014 that led to the creation of the Hashd al Shaabi force, which reports directly to the Prime Minister's office.

An Iraqi traffic policeman prepares to vote in Baghdad on May 10. Members of the security forces cast ballots before other voters.

Security fears

Security remained a big issue as Iraqis headed to the polls.

A statement released Friday by the Prime Minister's office urged voters to "choose the best for Iraq and for a brighter future" while also seeking to reassure them that they would be safe.

"We have ordered our heroic security forces to protect the electoral process, and to protect the voters and polling stations, and they are capable of protecting you," it said.

"Our heroic forces have achieved another victory by protecting the democratic process," Abadi said after the elections.

One candidate -- a college professor named Farouq Zarzour -- was assassinated this week in a town near Mosul. He was running for parliament as part of the National Coalition led by former Prime Minister Ayad Allawi.

A spokesman for ISIS also urged attacks against polling stations and voters in an audio message released last month.