The protesters were killed in a shooting in the city of Samawah, south of the capital Baghdad, the source told AFP.
A further 27 people were injured in the incident in front of the governor s headquarters, the source said without detailing who opened fire.
In Baghdad hundreds of protesters closed a highway at the entrance to the city s northwestern Shula neighbourhood, chanting “Iran, out out! Baghdad is free!” and “The people want to overthrow the regime”.
Demonstrations hit several provinces including Basra, despite Prime Minister Haider al-Abadi announcing fresh funds and pledges of investment for the oil-rich but neglected region.
Renewed clashes between security forces and protesters in Basra city left 50 people injured near the governor s headquarters, the majority protesters, a separate medical source said.
The internet was out of service across the country on Sunday for the second consecutive day.
Earlier on Sunday demonstrators tried to storm the Basra governor s headquarters but were dispersed by police who fired tear gas at them, an AFP reporter said.
Police also fired tear gas at stone-throwing demonstrators who tried to push their way into the Zubeir oil field south of the city, an AFP reporter said.
In Nasiriyah, provincial capital of neighbouring Dhi Qar province, 15 demonstrators and 25 policemen were injured, deputy health director Abdel Hussein al-Jabri said.
The clashes, including hand-to-hand combat, erupted when the demonstrators gathered outside the governor s office and pelted security forces with stones.
In Muthana province bordering Basra, hundreds of demonstrators gathered outside the governor s headquarters and some torched parts of the building, a police source said.
Protesters in Muthana also set fire to the offices of the Iranian-backed Badr organisation in the province s largest city of Samawa.
On Saturday, protesters had set alight Badr s headquarters in Basra, prompting authorities to impose an overnight curfew across the province.
As the protests continued Abadi met with security and intelligence chiefs in the capital Baghdad on Sunday, warning them to be on alert “because terrorists want to exploit any event or dispute”.
“Iraqis do not accept chaos, assaults on the security forces, state and private property, and those who do this are vandals who exploit the demands of citizens to cause harm,” he said.
The prime minister also ordered security services not to use live fire against the unarmed protesters.
The unrest erupted on July 8 when security forces opened fire, killing one person, as youths demonstrated in Basra demanding jobs and accusing the government of failing to provide basic services including electricity.
Two protesters died from gunshot wounds following rallies overnight Friday, although it was not clear who killed them.
At least 30 people were wounded on Saturday night in the central holy city of Karbala, where an AFP reporter said police fired into the air as demonstrators threw stones at them.
The demonstrations have also led to international flights to the shrine city of Najaf being cancelled, as the airport was closed after dozens of protesters forced their way into the waiting room Friday despite a heavy police presence.
Foreign airlines including Oman Air, flydubai and Royal Jordanian have all announced the suspension of flights.
The government s media office said Abadi has ordered the airport to reopen, without giving further details.
Protests continued Sunday morning in Najaf city, where an AFP correspondent said security forces dispersed a large demonstration.
A sizeable contingent from Saraya al-Salam, a paramilitary force loyal to prominent Shiite cleric Moqtada Sadr who won May elections, also deployed in the streets of Najaf.
The protests — which have spread north to Baghdad — come as Iraq struggles to rebuild after three-year war against Islamic State group jihadists, which has ravaged their country s infrastructure.
On Saturday evening, Abadi announced investment worth $3 billion (2.6 billion euros) for Basra province, as well as pledging additional spending on housing, schools and services.
“When the state responds to citizens demands it is a strength, not a weakness,” Abadi said during Sunday s meeting with top officials.
The country has been rocked by a series of conflicts since the 1980s and says it needs $88 billion to rebuild after the war on IS jihadists.
Officially, 10.8 percent of Iraqis are jobless, while youth unemployment is twice as high, in a country where 60 percent of the population is aged under 24.
The oil sector accounts for 89 percent of the state budget and 99 percent of Iraq s export revenues, but only one percent of jobs, as the majority of posts are filled by foreigners.