The deaths overnight in Maysan province on the border with Iran brought to three the number of demonstrators killed since the protests erupted Sunday in neighbouring Basra.

A spokesman for the Maysan health authorities, Ahmad al-Kanani, said the pair died from gunshot wounds in the provincial capital Amarah.

It was not clear who killed them but Kanani said there had been "indiscriminate gunfire" in the city.

Dozens more have been wounded in the past week, including security forces, according to medical sources.

The unrest comes as Iraq struggles to rebuild after a devastating three-year war against Islamic State group jihadists, and with the country in political limbo following May elections.

The demonstrations over unemployment, the rising cost of living and a lack of basic services escalated after a protester was killed by security forces on Sunday in Basra.

Demonstrators set tyres ablaze to block roads and tried to storm government installations.

On Friday Prime Minister Haider al-Abadi flew to Basra from Brussels, where he had attended a NATO summit, to try to restore calm.

But even as he met the governor of the oil-rich province and energy chiefs, protesters took to the streets of Basra city as well as other parts of the province and the unrest spread further afield.

Overnight in Maysan, several protests were held outside the headquarters of various political parties -- including Abadi's Dawa Party -- and some were set on fire, Iraqi media reported.

A small protest also took place after midnight in the northern Baghdad district of Al-Shula amid a heavy deployment of security forces, a security source told AFP.

- Protests spread to Baghdad -

The source said a few protesters were still out on the streets of Al-Shula on Saturday morning, adding that the demonstration was peaceful.

Unidentified calls were also posted on social media for massive demonstrations to take place on Saturday in Baghdad.

Some urged demonstrators to head for the fortified Green Zone, an area out of bounds for most Iraqis where the country's key institutions and embassies, including the US and British missions, are located.

On Saturday dozens of protesters rallied in different parts of Basra, including at the West Qurna and Majnoon oil fields west of the city, an AFP correspondent said.

Protesters were gathered at Basra's Umm Qasr port and outside the governor's office in the centre of the city. A group of demonstrators also staged a brief protest at the Safwan border crossing with neighbouring Kuwait.