Minister for the interior Christophe Castaner condemned the actions of a group of protesters captured on video by a nearby journalist.
The group - only some of which were wearing the distinctive “yellow vest” - were heard to be shouting “kill yourselves”, and other insults, to the law enforcement officers, in Place de la République in Paris.
The video emerged during the 23rd consecutive Saturday of the gilets jaunes movement.
It comes as suicide rates in the law enforcement community have been rising. Since January this year, 29 police officers have died by suicide.
In response to the video, Mr Castaner tweeted: “Shame on those who have behaved with such disgrace. Total support to our mobilised officers and their families. The vast majority of French people know what they owe them."
Honte à ceux qui se sont livrés à une telle ignominie !— Christophe Castaner (@CCastaner) April 20, 2019
Soutien total à nos forces mobilisées, et à leurs familles.
L'immense majorité des Français sait ce qu'elle leur doit.https://t.co/B8HZYV96NQ
The clash comes amid new violence during this weekend’s protests.
Several injuries were reported among protesters, with 14 injuries counted among members of law enforcement. There were 227 arrests, 163 people taken into custody, and 20,518 issued warnings.
According to government figures - always contested by protesters themselves - there were 27,900 people in total out across France, including 9,000 in Paris.
This marks a slight drop from the 31,000 overall last weekend, but a spike in Paris, after around 5,000 were counted in the capital last week.
Protesters clashed with officers across the city, with some fires lit in rubbish bins and cars, and some shops smashed - especially near Place de la République - as law enforcement used tear gas in some areas.
The movement was banned from converging around Notre-Dame, after rumours suggested that some would try to gather near the unstable, fire-damaged site. Police head Didier Lallement said this would amount to “pure provocation” on the part of the protesters.
The ban comes after several other areas of Paris, and certain districts of other cities, were also off-limits to protesters this weekend.
The centre of Lyon, the Place du Capitole in Toulouse, and the Champs-Elysees, were all subject to a ban on protests, after the measure was first introduced in March this year.
Bordeaux, Montpellier and Toulouse also saw significant protests of 1,500-3,500 people this weekend, while several hundred gathered in Marseille, Rouen, and Lille.
In Paris especially, protesters were understood to be demanding “a new ultimatum” to President Emmanuel Macron in the days following the Notre-Dame fire.
#MacronResign #Ultimatum2#YellowVests #Acte23 #Paris #MacronDemission #ActeXXIII #France #ViolencesPolicières#GiletsJaunes— Sarwar (@ferozwala) April 20, 2019
Millions for Notre-Dame, what about for us?': Yellow Vest fury explodes in Paris as anti-Macron activists clash with police ... pic.twitter.com/ZEZJ43d3qn
Mr Macron was forced to postpone his presentation of planned reforms after the national Grand Débat due to the cathedral disaster this week, and several clashes in Paris were understood to be a reaction to the many million-euro donations in the wake of the Notre-Dame damage.
Some demonstrators carried banners that referenced the fire, claiming that the wealthy billionaires who had donated to the rebuilding fund had not helped normal working people.
One sign read: “Millions for Notre-Dame, what about for us, the poor?”, while another said: “Everything for Notre-Dame, nothing for Les Misérables”, in reference to the Victor Hugo novel of the same name.
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