The number of deaths also did not rise by as many.
The first death was recorded on Monday in the southern region of Basilicata, meaning all Italy's 20 regions have now registered fatalities.
Medical experts confirm that Italy has focused its testing only on people showing severe symptoms in areas with high epidemic intensity like Lombardy, Emilia-Romagna and Veneto in the north of the country, thus it is hard to say the real numbers.
Italy has reported 743 new coronavirus deaths, as cases increased by 5,249 on Tuesday.
Health authorities have cautioned that it will be a few more days before they will know if Italy is at the beginning of a positive trend.
As in the previous days, the ISS chief also warned that a crucial goal for national authorities and the health system remain to be avoiding the dynamics of strong circulation of the virus seen in the northern regions "reproduced in the South".
In related daily news, Health Minister Roberto Speranza said the Italian Medicines Agency approved the testing of the antiviral drug known as Avigan against the COVID-19, local media reported. "Now, more than ever, the commitment of everyone is needed".
"We need more consecutive results to confirm the trend, to be more certain that we are in a favourable situation", he said. But for some older adults and people with existing health problems, it can cause more severe illness, including pneumonia. Almost 103,000 of the 392,000 people who have been diagnosed with the disease have recovered.
"Of the 50,418 people who are positive, some 26,522 are now under home isolation - being asymptomatic or with light symptoms - another 3,204 are in intensive care, and all the other hospitalized in ordinary wards", he specified.
Italy's daily deaths are still higher than those officially recorded in China at the peak of its crisis in Wuhan's central Hubei province. The number of fatalities dropped for a second day in a row, after reaching an all-time high of 793 on Saturday. The cities of Bergamo and Milan both showed signs of improvement, but the number of cases jumped significantly in Brescia, another hard-hit Lombardy city which registered 588 new cases Monday.
"Another lovely signal concerns the number of COVID-19 patients hospitalized (in ordinary wards), which is now 9,266, against 9,439 in the previous day.it is the first time", Gallera stressed.