Lucien Abenheim, the general director for health, told Health Minister Jean-Francois Mattei in a letter that he was tendering his resignation "given the present controversies surrounding the handling of the epidemic (of deaths) linked to the heatwave."

Mattei said it was possible the number of deaths from the two weeks of record-breaking temperatures, which ended late last week, had climbed dramatically past the government's previous estimate of 3,000.

"The figure of 5,000 was mentioned yesterday. It's one hypothesis. It's plausible but it's just a hypothesis," he told RTL radio, adding that precise figures would not be known for several weeks.

In his interview, Mattei also acknowledged criticism from doctors and the political opposition that the disaster had not been adequately handled.

"We didn't have the information and the warning signals that we should have had," he said.

"The health minister, who is before you now and who totally accepts his responsabilities, did not receive any warning signals," Mattei said.

As temperatures soared to around 40 degrees Celsius (104 degree Farenheit) in the first two weeks of August and the bodies of heatwave victims -- most of them elderly -- overfilled morgues and hospitals, the government was increasingly criticised for being too slow to react and underestimating the disaster.

The head of the administrative body that oversees the health system, Gilles Brucker, told Tuesday's issue of Le Monde newspaper there was "obviously ... a deficiency" in the way death tolls were reported.

"It isn't acceptable -- and in this we no doubt share some of the responsibility -- that the information in this area (hospital death tolls) was not shared immediately," he said.

"It isn't acceptable that people start to die in big numbers because of the heat without us, collectively, knowing about it so as to tackle the problem."

He said his National Health Oversight Institute would now develop ways for compiling and announcing in real time information about health crises in France's biggest cities.

Abenheim, who was in charge of Brucker's unit and other parts of France's general directorate of health, had in particular been criticised for failing to notify the government about the unfurling wave of deaths.

He said in his resignation letter, a copy of which was obtained by AFP, that he would continue in his job until a successor was found.

Abenheim's acceptance of blame followed attempts by the government to deflect accusations that it failed to sufficiently alert the public and reinforce health services until it was too late.

The left-wing newspaper Liberation mocked in particular Prime Minister Jean-Pierre Raffarin's statement at the weekend that French society -- and not the state health system or the lack of government leadership -- was to blame for the high death toll because it abandoned its elderly people.

The paper said Raffarin was trying to shift blame but that this tactic "was also part of the government's inadequate response to the consequences of the heatwave and its tardiness in recognising there was a public health problem that required a rapid and broad reaction".

Raffarin's centre-right government had cut budgets for the care of the elderly and "the dramas of old age didn't seem to be a priority for him just a few weeks ago", Liberation said.

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