"Given the current situation, the prefects will make decisions in co-ordination with mayors to protect our cities, public buildings and shops and - where necessary - even go so far as to ban certain gatherings and take all necessary measures," the president said in a televised address on Sunday evening.
Police work is also under scrutiny, Macron said and he had therefore asked the interior minister to look into it.
More than half a million people demonstrated in France on Saturday in a day of protest against the high cost of living.
Looting, arson and damage to property occurred in many cities, with masked rioters attacking town halls, police stations and other government buildings.
The dramatic collapse of a historical town hall tower in the city of Limoges, known for its porcelain, was posted all over social media, including cries of horror from residents who were shocked by the destruction.
"Yesterday, despite their professionalism, our law enforcement officers were confronted with unprecedented violence in numerous cities," Macron said.
"I have repeatedly asked the government to draw all the lessons from this regarding investigation and foresight, and to ensure that such a thing cannot happen again. I expect clear answers, and there will be full transparency."
The rioters would be punished and held to account, Macron said.
He added: "Anyone who destroyed something must pay for it. Anyone who looted must compensate for the damage. Anyone who tried to overthrow the republic will be held to account for it."
France was still reeling on Sunday from one of its most violent days of unrest in years after protests over high prices and public services left one demonstrator dead, thousands arrested and hundreds of police injured.
Demonstrations erupted into riots on Saturday, with a town hall torched, shops ransacked and buildings covered in graffiti as violent groups clashed with police in cities across the country.
One protester died after suffering a cardiac arrest during demonstrations in Paris.
Police made more than 2000 arrests across France while more than 600 officers were injured, the interior minister said.
"It's like a war zone here," said Dutch entrepreneur Tije De Boer, who had come to Paris with his children to visit a friend and said the protests forced him to flee his hotel at Place de la Republique, a trouble hotspot on Saturday.
More than half a million people joined marches in scores of cities, marking the convergence of a month-long student movement with broader social discontent against rising living costs and declining public services.
Saturday's unrest laid bare the deep anger at Macron, who leaves office in 2027 after a decade in power that has increasingly become defined by social discontent, a weak economy and ballooning debt.
The government has blamed the violence on "ultra-left" groups as well as criminals who it said instigated the looting.
While hundreds of thousands protested peacefully, violent fringe groups targeted public buildings, looted luxury boutiques and supermarkets, and attacked police vehicles and officers.
A massive clean-up operation began in cities from Lille in the north to Marseille in the south and Strasbourg in the east to Bordeaux in the southwest, where a masked mob invaded the residence of the local prefect.
Interior Minister Laurent Nunez said several hundred shops had been damaged on Saturday.
In Paris, smashed shop windows, burnt-out bicycles and spray-painted slogans bore witness to a day that began largely with peaceful demonstrations but descended into violence.
The unrest has increased pressure on Macron and his government ahead of a presidential election due next year.
Bordeaux mayor Thomas Cazenave said up to 100 stores had been looted in his city while Marseille mayor Benoit Payan announced emergency financial aid to support those businesses affected by the violence.
French retailer Carrefour's CEO Alexandre Bompard told French broadcaster BFMTV that 50 of the company's shops had been damaged, including 20 that were looted, with losses from the damage running into the tens of millions of euros.
with DPA
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