France has suffered an “exponential” increase in Covid-19 cases with 7,379 new infections in 24 hours, according to the country’s public health authority.

The number of new cases has been growing steadily throughout August, but jumped from 6,111 positive tests on Thursday and 5,429 on Wednesday.

Friday’s figure – the latest published by Santé Publique France – is the highest number of new cases in a 24-hour period since 31 March at the height of the epidemic

A check of historic data from the government’s Covid-19 website suggests it is the second highest since the figures began to be reported by the health authorities on 2 March.

However, the number of new patients admitted to hospital – 241 in 24 hours – remains relatively stable as does the number of admissions to intensive care, which rose by 34 patients.

The number of deaths attributed to Covid-19 rose by 20 in the previous 24 hours to a total of 30,596 since the start of the epidemic. There are 320 clusters under investigation, 31 more than the previous day. The percentage of positive tests is 3.9%.

During a long press conference on Thursday, French ministers admitted the August surge in Covid-19 infections could not be solely explained by an increase in testing, currently running at around 840,000 tests per week. The health authorities aim to reach 1m tests a week by the end of September.

Santé Publique France reported that “the dynamic of transmission [of the virus] is growing strongly and is very worrying”. There has been an increase in the number of infected people showing Covid-19 symptoms – as opposed to half being asymptomatic, as was reported the previous week. While all age groups are reportedly affected, the authorities say there is a continuing increase in cases among young adults, many of whom show no symptoms.

The rise comes at the end of the long summer holidays and just before la rentrée, the great return to work and school across France next week. All pupils are expected back at school on Tuesday or Wednesday, wearing masks if they are over 11 years old. All school and college staff must wear masks.

It is now obligatory to wear masks in outside public spaces in Paris and three city suburbs as well as Marseilles and Strasbourg. Faced with a surge in cases in the Grand Est (eastern France) the authorities in the Bas-Rhin have made it obligatory to wear masks outside in all towns with more than 10,000 inhabitants.