BAGHDAD: Iraq's prime minister demanded an immediate investigation into the deaths of two demonstrators on Monday, even as he faced the same accusations as his predecessor over protest-related violence.

The deaths threaten to reignite an unprecedented protest movement against government graft and incompetence that erupted across Baghdad and southern Iraq in October but had waned in recent months.

On Sunday, Iraqis staged angry rallies in the capital and several southern cities, where temperatures topping 50 degrees Celsius (122 Fahrenheit) have swelled demand for air-conditioning and overwhelmed dilapidated power grids.

The deaths prompted outrage at Prime Minister Mustafa al-Kadhemi, with activists accusing him of failing to stop a heavy-handed police response to the rallies.

He gave a rare televised address on Monday evening, saying Iraqis have "a legitimate right" to protest.

"Security forces are not permitted to fire a single bullet against our brothers, the demonstrators," Kadhemi warned.