"We are seeing a wave faster than all the previous ones," Attal said while addressing a press conference late on Monday.
He noted that the incidence rate has spiked by nearly 125 per cent in one week, "an increase so strong, so sudden that we had never known since the beginning of the epidemic in our country", reports Xinhua news agency.
"For several days we have crossed the threshold of 10,000 positive cases every day. This virus contaminates at lightning speed."
The Delta variant now accounts for 80 per cent of the overall infections in France, he added.
The overall caseload and death toll currently stood at 5,931,923 and 111,678.
Since July 12, the number of departments exceeding the alert threshold of 50 infections per 100,000 inhabitants has increased from 12 to 37, according to data released by the Health Ministry.
The surge mainly concerns the overseas departments, the Paris region and the coast, where there are many tourist arrivals during the summer period.
The government spokesman called for everything to be done so that the fourth wave would not be "more devastating" than the previous ones.
Earlier on Monday, a cabinet meeting adopted a law bill containing new measures intended to contain the rapid spread of the virus, including compulsory vaccination for caregivers and massive extension of the health pass, announced by President Emmanuel Macron last week.
Under the bill, a compulsory health pass for access to cultural and leisure venues will come into force on Wednesday, certifying that the bearer has either been fully vaccinated or had a recent, negative PCR test.
For bars and restaurants and certain shopping centres, "the pass will be due on August 30, the time for those who wish to be vaccinated", Attal said late Monday.
The bill, to be presented to Parliament at the end of the week, also included an obligation of 10-day isolation for people who test positive for the virus.
There will be checks and sanctions for non compliance with the health pass rules, with a fine of up to 1,500 euros for a natural person and 7,500 euros for a legal person at the first breach, said Attal.
At the third breach, it can go up to one year in jail and a fine of 9,000 euros for a natural person, and one year in jail and 45,000 euros for a legal person, he added.
Warning about the risk of a new variant if the virus circulates too much, Attal said "vaccination coverage is not sufficient" in France.
Till date, 30.79 million people in France have completed their vaccination, representing 45.7 per cent of total population.