Health minister Olivier Véran has written to health workers saying he will not accept any violence, intimidation, attack on them.
Nationwide protests against the introduction as of Monday in France of the requirement to carry a 'health pass' showing that a person has no coronavirus infection, or has had a double Covid jab, when entering public venues or before boarding trains and planes drew around 237,000 people, according to official estimates.
More than 200,000 people, according to official figures, took part in marches around France this weekend protesting against recently introduced measures which require a person to carry a health pass showing they are free of coronavirus infection or vaccinated before entering a wide range of public venues.
An official with France's interior ministry said 161,000 people had demonstrated across the country on Saturday.
Demonstrations in Paris and other cities over plan for mandatory vaccinations for health workers and vaccine pass for public places.
Some demonstrators waved Russian flags and held banners calling for greater cooperation between Mali and Russia.
Protestors are unhappy over recent rejection by French constitutional court of parts of a law intended to protect regional languages.
The decision not to try Kobili Traoré over 2017 killing of Sarah Halimi, 65, has provoked international outrage.
Demonstrators, including gilet jaunes or 'yellow vest' activists, also protested against Covid restrictions.
Proposed legislation to ban the dissemination on social or traditional media of police officers' faces, justified as protecting the safety of police staff, and which would apply to civilians and journalists alike, has prompted street protests in Paris and other cities across the country over what demonstraors say is a law which would gag disclosure of police abuses.
There were more fierce protests and calls for a boycott of French goods in Muslim countries on Monday following President Emmanuel Macron's defence of the right to publish cartoons of the prophet Muhammad during a homage to teacher Samuel Paty who was beheaded by a fundamentalist for showing the cartoons to his pupils in a lesson on civic rights and free speech.
Meanwhile the number of new COVID-19 cases in France rose by 10,561 on Saturday - the highest daily number since the pandemic began.
Protesters marched through Paris with signs reading "Laissez nous respirer" ("Let us breathe") in reference to George Floyd, and protests also took place in the UK.
A procession of around 15,000 people, according to official estimates, marched through central Paris on Saturday, along with several thousand in other cities and towns across France, protesting racism and police violence in the country and highliting the case of a black man who died in strikingly similar circumstances to Afro-American George Floyd in Minneapolis last month.