For the sixth night running police officers demonstrated in Paris on Saturday, marching from the Place de la République square to the scene of last November's Paris attacks.
There were other protests in Evry, near the scene of a Molotov cocktail attack that left four police officers injured and one fighting for his life, and in the eastern cities of Nancy and Strasbourg.
On a visit to a police station in Tours, western France, at the weekend, Prime Minister Manuel Valls, appealed to the police to "continue the dialogue" after their unions' meetings with Interior Minister Bernard Cazeneuve and Justice Minister Jean-Jacques Urvoas this week.
"I'm a former interior minister and I know how much we owe to the bravery of our police, our gendarmes and our firefighters," he tweeted.
Hollande to meet unions
In a sign of how seriously the government takes the unrest, the unions are to meet President François Hollande at the beginning of the week.
A coalition of unions has called for silent protests in front of courthouses every Tuesday, while another has organised a "march of anger" on Wednesday, an initiative its rivals claim is an attempt to take over a movement that appeared independently.
National Police Chief Jean-Marc Falcone has also lost authority with the rank and file.
Chants of "Falcone resign!" have been heard since he dubbed it "unacceptable" that officers demonstrated in uniform and used police cars, in breach of rules, during the first of the Paris protests.
List of demands to be compiled
Nevertheless, Falcone has been charged with touring the country to compile a list of the force's grievances, which he is to submit to Cazeneuve on 15 December for action at the beginning of next year.
Valls on Saturday promised to give the police more resources.
Ageing cars and buildings are among the protesters' complaints but questions of safety and job satisfaction seem to be more important to them.
One demand is for fewer days on guard duty, for example outside police stations or at sites at risk of terror attacks, because officers believe it turns them into targets.
Self-defence, weapons, impunity
Others are for an extension of the right to carry a weapon, tougher sentences for the crime of insulting police officers, the reinstatement of minimum sentences for physical attacks on them and an end to alleged "impunity" for criminals such as those who committed this month's firebomb attack.
Falcone told Sunday paper Journal du Dimanche that he was not in favour of revising the law on legitimate defence "at this point", given that it was changed in the anti-terror law passed in June.
Urvoas has claimed that sentences for assaults on police are in fact much more severe than on other assaults and has promised to provide figures to prove it.
The claim of impunity is also not justified, he told La Croix newspaper, and proposed to ensure that courts inform police of the results of arrests.