"These coming days will be the hardest because infections have not reached the most acute phase yet and the numbers will continue to grow", he told La Stampa newspaper.
Conte said he expected the restrictive measures taken by his government to contain the epidemic to start showing results in the next few days.
"We took it one step further by stopping all non-essential production activities... But a lot depends on how responsible we are about restrictions. If we all follow them, if everyone pulls their weight, we will get through this toughest challenge sooner", he said.
Italy overtook China last week as the country to record the highest virus-related death toll and is now the worst-hit European country. The Italian government has put the nation into a lockdown, banning any movement inside the country.
Italy has recorded more than 59,000 cases of infection with the virus, and 5,476 people have died from COVID-19, while more than 7,000 have recovered.