The election, which will help determine whether Iraqi Prime Minister Mohammed Shia al-Sudani gets a second term, comes against the backdrop of fears of another conflict between Israel and Iran, and Iraq's balancing act with Iran and the United States.
An estimated 1.3 million army and security personnel and about 26,000 displaced people are eligible to vote.
There are 7744 candidates competing in the election, most of them from largely sectarian-aligned parties.
Election day is set for Tuesday.
Yazidis, many who fled their homes over a decade ago after attacks by the Islamic State group, voted at a camp near Dohuk in the semi-autonomous northern Iraqi Kurdish region.
Many have still not been able to return home because of political disputes and lack of infrastructure.
A polling station set up in a small Dohuk school stood almost empty until after 9am when more voters began to appear, some clutching worn ID cards and others guiding elderly relatives toward the entrance.
Inside, the classrooms were crowded with dozens of monitors from rival parties and candidates.
During their terror campaign, IS militants rampaged through Iraq's Sinjar district in Nineveh province, killing and enslaving thousands of Yazidis who the extremist group considered heretics.
Since the defeat of IS in Iraq and Syria, members of the Yazidi community have been trickling back to their homes in Sinjar but many see no future there.
There is no money to rebuild destroyed homes, infrastructure is still wrecked and multiple armed groups have carved up the area.
The area has also been caught up in political disputes between the central government in Baghdad and authorities in the Kurdish region wrestling over Sinjar, where each backed a rival local government for years.
"Eleven years passed and the situation is the same," said Khedhir Qassim, a displaced Yazidi from Sinjar who voted at the camp in Dohuk, saying he has little faith that new leaders will bring change.
"We want them to support us and rebuild our areas that are ruined due to their political dispute and where everyone works for their own benefit," he added.
Edris Zozani, another displaced Yazidi who voted in the camp, said he voted for the Kurdish Democratic Party, one of the two main Kurdish parties in the country, which holds sway in Dohuk.
"If we have independent Yazidi candidates, they wouldn't be able to represent us effectively," he said.
"But if they go to parliament as part of strong lists, like the KDP, they would be in a better position to support the Yazidi community."
In the Iraqi capital, Iraqi soldiers and police voted, as well as members of the Popular Mobilisation Forces, a coalition of primarily Shii'te, Iran-aligned militias that united to fight IS.
The coalition was formally placed under the control of Iraq's military in 2016 but in practise still operates with significant autonomy.
Several of the armed groups making up the PMF have associated political parties that are participating in the elections.
