More draconian lockdown measures are expected to be imposed soon in Italy.
Those measurements are likely to prevent further spread of the deadly virus in various parts of the country
Italy on Thursday overtook China's coronavirus death toll, with 427 new fatalities taking its total since the first case was registered in February to 3,405.
China has officially reported 3,245 deaths since registering the first infection at the end of last year.
Italian authorities are threatening to introduce even more draconian measures after several days of grim numbers in its battle against the outbreak.
Supermarket opening hours could be curtailed and people banned from taking a stroll or going for a run, something that has been a grey area until now.
Italians are already into their second week of lockdown.
Among the worst-hit cities are Bergamo and Brescia in the north. In Bergamo, the cemetery is under such pressure that more than 60 coffins were transported to cemeteries in other cities by a convoy of military trucks on Wednesday evening, according to the Daily Telegraph.
Although the rate of infections is slowing, down from 12.6 percent on Tuesday to 8.4 percent on Wednesday, the authorities say there are still too many people out on the streets, elevating the risk of spreading the virus.
More than 35,000 Italians have been infected with the virus so far, although 4,000 of those have recovered.
Around a million people have been questioned by police and soldiers since the coronavirus lockdown was imposed in Italy, of whom 43,000 were charged with having no valid reason for being out of their homes. That is less than five percent, but politicians and doctors say it is still too many.
People need to stay at home "or we will be forced to take more rigorous measures", said Attilio Fontana, the governor of the northern Lombardy region worst hit by the pandemic.
A spell of beautiful weather has not helped, tempting people out of their homes to enjoy the sunshine, blue skies, and blossoming trees.
"On the one hand I see people going for a stroll, and on the other, I'm seeing people [in hospital] who are unable to breathe," Mr. Fontana told Corriere Della Sera. "Enough. If the current measures are not sufficient, we will have to intervene further.
"The numbers from this epidemic continue to be extremely worrying. I cannot accept that so many people are dying each day. And I get angry with those who still don’t get it, or pretend not to.
"We are asking people to stay at home not because we enjoy being buddies but because this is the only weapon we have to stop the spread of the contagion."
He said the situation remained "terrible", with exhausted doctors and nurses performing "superhuman" feats as they try to save as many people as possible. Many have been working "under extreme stress" for three weeks, practically without a break.
The minister for sport also called on Italians to give up physical activities to try to stem the spread of the virus.
"These are the most dangerous days and I do not see the need to do physical exercise outside the home," said Vincenzo Spadafora. "If we need to take tougher measures, we will do so."
The lockdown is meant to end on April 3 but looks almost certain to be extended, as will the closure of schools.
Several ministers have dropped hints in recent days that the unprecedented peacetime measures will be prolonged. Paola De Micheli, the transport minister, said she "does not rule out" the extension of the shutdown, which has left millions of families confined to their houses and apartments.