"We managed to rescue 11 babies, 107 women and 28 staff" after the 3:50 am (0250 GMT) fire in the hospital in Oued Souf, 500 kilometres (300 miles) southeast of Algiers, spokesman Captain Nassim Bernaoui told AFP.
26 pupils, two teachers killed in Liberia school fire
"Unfortunately we regret the deaths of eight babies, some from burns and others from smoke inhalation."
Dozens of fire engines were deployed to bring the blaze under control.
The cause of the fire was not immediately clear, Bernaoui said.
Prime Minister Noureddine Bedoui ordered an inquiry and sent Health Minister Mohamed Miraoui to the scene of the fire.
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