Speaking at a ceremony held before parliament's summer recess, Mattarella stressed that everyone should continue to take basic precautions to combat the spread of the virus, such as social distancing, the use of facemasks in enclosed spaces, and washing hands frequently.
Mattarella paid tribute to the more than 35,000 people who have died in Italy due to Covid-19 to date, saying “four months ago over 800 of our compatriots died in just one day,” the Ansa news agency reported.
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“This is a reason for us to not lower out defences,” he said. “Learning to live with the virus does not mean behaving like it no longer exists”.
“One must not confuse liberty with the right to make others ill,” he said, apparently referring to recent criticism of the precautions by some opposition politicians and other public figures.
“Out of respect for the dead, we cannot and must not undo the sacrifices made by our fellow citizens, whose behaviour allowed us to have greater confidence today.”
“Elsewhere, refusal or inability to follow those behaviours is causing dramatic consequences,” he added.
The president also thanked the countries that came to Italy's aid at the peak of its coronavirus emergency.
His words echoed the warnings of Italy's health minister and other public health officials, who have repeatedly warned Italians in recent weeks to remain vigilant amid fears of a potential second wave of infections across Europe.
Offical data shows that the infection rate in Italy has remained generally stable overall during the past month.
A slight rise in new cases was reported on Thursday as Italy registered 386 new coronavirus cases in 24 hours, and the number was similar on Friday at 379.
This was up from the 289 cases reported on Wednesday, according to the Health Ministry.
Most of Thursday's new cases were in Veneto (112) and Lombardy (88), with 39 in Sicily and 35 in Emilia-Romagna.
Five regions reported no new cases: Umbria, Sardinia, Valle d'Aosta, Molise and Basilicata.