The number of cases has reached 1,128 since the start of the epidemic a week ago, up from 888 on Friday.
Around half those tested show few to no symptoms, the Italian health authorities said.
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Official figures said 105 people were receiving intensive care hospital treatment as of Saturday.
Eighty of the most serious cases are in the northern Lombardi region. All the deaths have been recorded in three northern regions, the health ministry’s figures showed.
A total of 1,049 people remained infected on Saturday, the figures showed.