In recent weeks, some of the protests have turned into major riots described as the most violent clashes in France in decades.
On Saturday, protestors in Paris smashed the gates to a government office and cars and motorbikes were set alight.
"The government is in favour of our law being amended and punishing those who do not respect this obligation to declare protests, those who take part in undeclared protests, those who arrive at protests with balaclavas", added the prime minister.
Philippe said 80,000 members of the security forces would be deployed for the next expected wave of protests, adding that "those who question our institutions will not have the last word".
French President Emmanuel Macron's approval rating now stands at 28 percent, improving by five points in a month and marking the first improvement in ratings since the start of the nationwide yellow vest protests in November, an Ifop-Fiducial poll showed.
The "yellow vests" movement - named after the fluorescent jackets all French motorists have to carry in their vehicles - started in mid-November as a protest against a fuel tax but have since grown into a broader backlash against the government.
Christophe Dettinger, who was twice national light-heavyweight champion, was caught on camera jumping over the railings of a pedestrian bridge blocked by baton-wielding police before swinging blows at the officers, forcing them to retreat.
"Yellow vests, do not weaken!"
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Much of that came with Timberwolves star Karl-Anthony Towns on the bench. "I hope he gets healthy soon and comes back stronger". I said: "I don't know what's wrong with him he was just getting ... acting insane for no reason", he said on Twitter.
Known as "The Gypsy From Massy", the 37-year-old man had turned himself in on Monday and remained in police custody.
While the number of protesters has dwindled since the earliest demonstrations, a smaller but increasingly radical core seem determined to push on.
The "yellow vest" movement mobilized through social media has forced Macron to reconsider his economic and social recipe for the eurozone's No.2 power by offering a series of concessions to appease angry citizens.
Budget Minister Gerald Darmanin sought to distinguish genuine protesters, who want lower taxes and more help for low-income families, from those "who are in the business of ultra-violence".
Public anger appeared to have abated over the holiday period; however, the brief arrest on Wednesday of Eric Drouet, one of the leaders of the movement, seemed to have rekindled resentment among his supporters.
The move led to criticism from political leaders on the far right and radical left, who have encouraged demonstrators to continue taking to the streets to underline their discontent with Macron's agenda. "It needs to end", he told RTL radio on Monday.
"Yellow vests, do not give up!" Law professor Giuseppe Conte has been chosen as Italy's new prime minister by the leader of the 5-Star Movement, Luigi Di Maio, and League leader Matteo Salvini.