French authorities first put the death toll in single digits, then raised it to 50. After a doctors' group faulted that figure as too low, the health ministry estimated last Thursday that 1,600 to 3,000 people died from heat-related causes starting on Aug. 7.
Mattei then said on Monday that it was "plausible" that up to 5,000 people may have died. But he said the figure was a "hypothesis" and said a final toll was not expected for several weeks.
Temperatures have cooled considerably across France since the first two weeks of August, where parts of the country suffered under heat of more than 40?C.
The heat wave caused morgues and funeral homes to overflow with bodies last week, and hospital hallways were jammed with patients on stretchers because there were not enough beds.
French meteorologists say the hot spell was the longest and hottest on record, and many other parts of Europe also roasted. The heat also fanned forest fires and devastated livestock.
Meanwhile, an Italian public-advocacy group called on Wednesday for a government inquiry into heat-related deaths in Italy, saying the number could be in the thousands.
The Italian Health Ministry has refused to release any official figures, saying it was almost impossible to determine whether deaths -- particularly those of the elderly or gravely ill -- were directly linked to high temperatures.
The Italian daily La Republica has reported that heat-related deaths numbered at least 2,000. Many other Italian papers have published similar estimates.
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