Nigerian President Muhammadu Buhari on Sunday appealed for "peace" as authorities struggled to halt looting across the country, the latest in a wave of unrest sweeping Africa's most populous nation.

A statement from the presidency said Buhari backed a judicial inquiry in Lagos "to give justice to peaceful protesters who lost their lives, security men who were murdered" and those who lost property in days of violence.

The leader "appealed to the people all over the country to maintain peace and brotherhood as the machinery of the government and the wheel of justice turn against the perpetrators", it said.

Peaceful demonstrations against police brutality erupted in Nigeria on October 8 and quickly snowballed into one of the biggest challenges to the ruling elite in decades.

Chaos spiralled after security forces on Tuesday opened fire on peaceful demonstrators in the centre of Lagos, sparking international outrage and days of rioting in Africa's biggest city.

Buhari has faced fierce criticism for failing to publicly address Tuesday's shooting of protesters, in which Amnesty International says the army and police killed 12 people.

The presidency statement said he had "all along avoided going into a debate" over the incident "until all the facts are established".

The situation has calmed in economic hub Lagos after days of violence that saw official buildings torched, supermarkets looted and vehicles destroyed.

Peaceful demonstrations against police brutality erupted in Nigeria on October 8 and quickly snowballed into one of the biggest challenges to the ruling elite in decades   
Peaceful demonstrations against police brutality erupted in Nigeria on October 8 and quickly snowballed into one of the biggest challenges to the ruling elite in decades    AFP / Sophie Bouillon

But authorities over the weekend struggled to halt a wave of looting in a number of regions as crowds defied curfew orders to ransack government warehouses.

Governors have slapped round-the-clock curfews on a string of states as residents have pillaged stocks that were meant for distribution during coronavirus lockdowns.

Locals raided agricultural supplies in the central city of Jos on Sunday a day after thousands had emptied a vast government warehouse.

Looting of food supplies was also reported in Taraba and Adamawa states.

Amnesty International says a total of 56 people have died since the demonstrations began less than three weeks ago.

The authorities have insisted that the protests were "hijacked" by criminals but demonstrators say officials were trying to undermine their demands for change.

The presidency said 229 suspects accused of looting and destroying property were set to face prosecution in Lagos.

Nigeria is a tinderbox of deep social and economic grievances with around half of the estimated 200 million population living in extreme poverty.

Frustration runs deep among younger generations furious with the country's graft-riddled leadership over a lack of opportunities.