The French health ministry has said the deaths of up to 3,000 people in recent weeks could be attributed to the European heat wave.
The elderly have suffered most
The announcement came as the government extended throughout the country an emergency hospital plan originally introduced in the Paris region to deal with the medical crisis.
The move was ordered by Prime Minister Jean-Pierre Raffarin, who cut short his holiday to head a crisis meeting of his cabinet in Paris.
The "Plan Blanc", which is normally reserved for epidemics, disasters or terrorist attacks, provides for the recall of doctors from holiday and making available extra staff, hospital beds and temporary mortuaries.
Correspondents say the measure is an attempt by the government to show it is not taking the problem lightly, after sharp criticism from the socialist opposition and health professionals.
The fatality figures were the first to be given by the government, which previously said that there was no accurate way of measuring deaths from the heat.
The ministry said its estimates were based on reports of deaths received from hospitals and mortuaries whose figures for this week were 37% higher than for the same period last year. The figure for Paris was more than 50% higher.
The heat eased slightly on Thursday, with temperatures in Paris reaching around 30C compared with more than 40C earlier in the week.
Temporary mortuaries have been set up
And forecasters predicted relief across western Europe, with the UK, Germany and Spain also looking forward to cooler, fresher weather in the coming days.
The extreme heat has set records on the continent, leading to dozens of deaths from heat stroke and devastating forest fires in countries on the western Mediterranean.
Firefighters are continuing to battle blazes in Portugal, where the popular tourist region, the Algarve, remains under serious threat.
French officials say comprehensive nationwide casualty figures will be released next week, based on a survey of private and public medical institutions including retirement homes.
But the BBC's Alan Little in Paris says the health ministry's announcement is a humiliating turnaround for a government whose response to the crisis has been perceived as too slow.
Most ministers have been out of Paris for the traditional August holiday.
Health Minister Jean-Francois Mattei told French radio the government "carried out the responses that were needed".
Most of the victims are old people, prompting comments in the press to the effect that the real scandal was their loneliness and isolation - many families leave behind their elderly relatives as they go on holiday.
However, Dr Muriel Chaillet of the St Antoine hospital in Paris told BBC News Online that the situation could be blamed partly on an aging population but partly on the state of the health service.
"Last summer the situation was catastrophic and this year it is worse; we were not at all prepared. The hospital system is failing," she said.
"These figures panic me, but they do not surprise me; they correspond to the situation."