"The extreme heat of recent days has a delayed impact, particularly on vulnerable people but also on some younger ones, who end up in the emergency room five to 10 days after the heatwave," Rist told La Tribune newspaper.
"We're seeing indicators that mortality will very likely be higher than at the same time last year."
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French authorities said on Thursday that hospitals in and around the capital Paris were reaching "saturation point".
But the minister warned that pressure on already overwhelmed hospital facilities is likely to continue even after temperatures drop.
The effects of the heatwave for patients with chronic illnesses "can last for several weeks."
"But providing reliable figures takes time. Only 60 percent of death certificates are issued electronically. We have to wait for the paper certificates to come in," she said.
The minister said she would then make the figures public "with full transparency" using the "most reliable figures possible".
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