"I will never accept violence", he said.
He said those responsible did not want change, but instead meant to "wreak chaos". He refused to answer any questions from journalists about the situation in Paris.
Dozens of cars were torched by the gangs of rioters, some of whom wore gas masks and ski goggles to lessen the effects of tear gas which was sacked continually by police. Some will be brought up for trial as soon as Monday, according to the minister.
The president's office issued a statement after an emergency meeting was held at the presidential palace Sunday to discuss the protests a day earlier in which activists wearing yellow jackets trashed the streets of Paris.
The level of violence on Saturday was too much for some of the Yellow Vests themselves.
Delpuech said some participants in Saturday's rioting used hammers, gardening tools, bolts and aerosol cans in clashes with police.
President Emmanuel Macron rushed to the Arc de Triomphe on Sunday after one of France's most revered monuments was vandalized by rioters, with the government considering a state of emergency after the worst bout of unrest for years.
The French government says it is considering all options to control the protests and stem the violence.
A broken sculpture of Marianne, a symbol of the French Republic, appears damaged in the gallery inside the Arc de Triomphe during a demonstration Saturday, Dec.1, 2018 in Paris.
Paris police Prefect Michel Delpuech said some officers described encountering "unprecedented" violence, including protesters using hammers, gardening tools, bolts, aerosol cans as well as rocks in physical confrontations.
Protesters, including some wearing black hoods, piled up large plywood planks and other material in the middle of a street near the Arc de Triomphe, and set the debris ablaze.
Many on the outskirts of smaller provincial towns and villages have expressed anger, underlining the gap between metropolitan elites and working class voters that has boosted anti-establishment politics across the Western world. Many protesters chanted that Macron should resign. He will not "speak to the nation", Al Jazeera reports, but he did visit the Arc de Triomphe Sunday morning, where he viewed the damage. Even luxury shops on nearby rue Faubourg St. Honore, where no protests were expected, were closed Saturday and their windows boarded up.
"We are ready to talk to them everywhere and the door is open to them", Griveaux said.
Mr Griveaux added that the president was ready for dialogue with the Yellow Vest protesters - but will not back down from his green agenda.
At a planned meeting on Friday between the movement and the prime minister, only two representatives showed up and one quickly left, saying his request that the meeting be televised live had been rejected. They were then dispersed by police. People work and pay a lot of taxes and we are fed up, ' said Rabah Mendez, a protester who came to march peacefully in Paris. The Paris police department said 205 people had been arrested including militants from the far-right and far-left.
However, despite Macron having public support hovering at around 25 per cent, he is only one and a half years into his five-year mandate and has considerable support in the French legislative assembly.
Enraged protesters in France have objected rising taxes in the country and Macron's leadership, which led to the arrest of at least 107 demonstrators.
"The people are in revolt", she said.
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