Since October 30, France has been placed in new nationwide confinement, effective until early December, which locked down 67 million inhabitants, who can go out only to work, buy essential items or for a health emergency.
All non-essential businesses such as restaurants, cafes, bars, cinemas and gyms are closed.
Castex said his government has decided to "keep the confinement rules unchanged, at least for the next 15 days".
"The challenge for the coming days is not to relax our efforts but to reinforce them," even though there were signs of a slowing spread in France, he said.
The number of confirmed cases fell by 16 per cent in a week.
The key reproduction rate, also known as "R" which measures how fast the virus is spreading, is below 1 across the country, official data showed. It means each person who caught the virus is infecting less than one person.
The national lockdown "seems to produce its first effects", said Castex.
"But we remain cautious...This recent trend is fragile and can only produce results if it is confirmed over time."
If the virus spreads further in the coming days, the government could impose more restrictions, Castex warned.
Official data on Thursday revealed that 33,172 people tested positive the virus in the last 24 hours, taking France's overall infection tally to 1,898,710.
The daily figure was lower than the 35,879 new cases registered on Wednesday, and much lower than the daily record of 60,486 cases reported on November 6.
In the same period, there were 425 new fatalities,which increased the death toll to 42,960.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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