The deaths threaten to reignite a country-wide protest movement that erupted in October over government graft and incompetence but had died down in recent months.

On Sunday, demonstrators staged angry rallies over power outages in the capital and several southern cities, where temperatures topping 50 degrees Celsius have overwhelmed electricity generators.

In Baghdad, dozens gathered at the protest hub of Tahrir Square, clashing with police and other security forces stationed there.

An AFP correspondent saw the burnt remains of tent structures in the square on Monday morning.

"Two protesters died this morning. One was shot with a tear gas canister in the head, and another in the neck," a medical source told AFP on Monday.

The two victims are the first since Prime Minister Mustafa al-Kadhemi, who had promised a dialogue with protesters, took office in May.

In a statement overnight, his office acknowledged "unfortunate events" in protest squares, but insisted security forces had been instructed not to use violence unless absolutely necessary.

It said the government would carry out an investigation into Sunday's events to hold those responsible to account.

But online, activists were already comparing Kadhemi to his predecessor Adel Abdel Mahdi, who stepped down last year following months of protest-related violence.

Around 550 people were killed in that wave of rallies and another 30,000 wounded, many of them by military-grade tear gas canisters that can pierce human skulls if fired directly rather than lobbed at an arc to disperse crowds.

There was virtually no accountability for those deaths under Abdel Mahdi; Kadhemi had pledged to publish a list of all the victims, carry out investigations and open a dialogue with protesters.

But a cartoon shared online on Monday morning showed a caricature of Abdel Mahdi handing over tear gas canisters to his successor.