France on Saturday reported 319 more deaths in hospital caused by the coronavirus, bringing the total toll of the epidemic in the country to 2,314.

Prime Minister Edouard Philippe warned that the "battle" against the virus in France was only just starting, warning the first two weeks in April would be even tougher than the last fortnight of March.

There are now 37,575 confirmed cases of coronavirus infection in France, up 4,611 on the day before, according to a daily update published by the government.

There are now 17,620 people in hospital, with 4,273 of them in intensive care, it added.

Both the death toll and the number of infections are likely higher than the official figures. The number of those who died counts only those who died in hospital -- not retirement homes or at home -- while only those deemed at high risk are currently being tested.

"I want to say how things are with clarity and frankness. The battle is only starting," said Philippe at a news conference with Health Minister Olivier Veran to outline the government's strategy. "The first 15 days of April will be even more difficult than the 15 days that are coming to an end now," Philippe said.

He said France's twin aims were to increase its intensive care capacities and to flatten the curve of the virus's spread. Veran vowed that France would ramp up its testing in the weeks to come, promising that there would be 50,000 traditional tests and 30,000 rapid ones carried out daily by the end of April.

He said that after placing an order for five million rapid tests, France would be able to carry out 100,000 such tests daily by June.

With the government criticised for a lack of sanitary masks -- especially for health workers -- Veran added that France had now ordered a billion of them, including notably from China. He said that France was only able to produce eight million masks a week. "Our reserves are not infinite," he added.

The pair's press conference in Paris was given to just one journalist, who pooled questions from colleagues, as a health precaution. France has been in lockdown since March 17 in a bid to slow the spread of the epidemic and officials have repeatedly warned it will take time for the measures to bear fruit.

Philippe had announced on Friday that the lockdown would be extended by another two weeks to April 15 given the gravity of the crisis.