According to data compiled on Thursday evening, 9,843 new infections have been confirmed in France in 24 hours.
This is the highest number of new cases since France expanded its testing.
Castex warned that, for the first time in several weeks, the number of hospitalized Covid-19 patients would increase and the virus would again affect the elderly and other groups at increased risk.
The Prime Minister said that more than a million Covid-19 tests are now being performed a day, but he acknowledged that the results were not ready soon enough for those who needed them most urgently, namely people with Covid-19-specific symptoms, people who had contact with an infected person and medical personnel.
Box said that the testing process for these groups would be accelerated.
He emphasized that the situation in Bordeaux and Marseilles and Guadeloupe was of particular concern.
The Prime Minister said that he had instructed the local authorities to come up with new measures to limit the spread of the virus by Monday.
The box also said it would recruit 2,000 new staff to track the contacts of infected people.
He said that the self-isolation period for contacts would be reduced from 14 days to seven, but that it would be checked for compliance.
Many doctors fear that in the next three months, intensive care units may again overflow with patients infected with Covid-19, as it was in March.
In France, it is still forbidden to gather large numbers of people, and in many large cities, including Paris and Marseille, face masks are also a mandatory requirement on the streets and in parks.
Kastex called on the public to abide by the requirement to wear masks and social distancing rules, and said that older people should be especially careful.
