In an interview with France Inter, Jean Castex said people who resisted mask-wearing, now compulsory in the workplace, enclosed public spaces and on public transport, should “think of others”.
“They all have vulnerable and elderly people in their families. People feel invincible and think that they do not need a mask.
“People will contaminate others,” he warned. “I appeal to a sense of responsibility.”
Castex said the French government alone could not bear all responsibility for curbing the outbreak, and “everyone must feel invested in the fight against the epidemic.”
France on Tuesday reported more than 3,300 new infections in 24 hours, with new admissions to hospital and intensive care also continuing an upward trend observed in recent weeks following a dip brought about by a near two-month social lockdown.
Separately, France's government spokesman Gabiel Attal said that local authorities in Paris and its surrounding suburbs may be looking at introducing reinforced rules in the coming days.
This comes as local authorities in Marseille bring in bar closures and extra mask rules. Marseille and Paris are among the 10 'red zones' of France that have high infection rates.
Asked whether the government could issue new stay-at-home orders if the situation spirals out of control, Castex said on Wednesday “all hypotheses” were on the table, though a new lockdown was “not the goal” given the severe economic impacts.
The government is to unveil details of an economic revival plan worth some €100 billion on Thursday next week, and Castex announced the cultural sector would receive €2 billion to cover lost revenue.
He added a 5,000-person limit for concerts and sporting events will remain in place and local authorities in red zones will no longer have the power to grant exceptions to the attendance limit.
Given that no proven vaccine or cure exists, Castex warned the population must learn to “live with the virus”.
But life also has to go on, and Castex said the government would do all it can for the French to resume work, school and social and cultural participation “as normally as possible”.
Masks are being made compulsory for children aged 11 and older when they return to school next week and will be provided for free to those at particular risk or cannot afford it.
But “we are not going to pay for masks for families that don't need” assistance, said the premier.
Masks are now compulsory in the busiest areas of many French towns and cities, including the capital.