Imposed nationally on March 12, the shutdown of most businesses and a ban on public gatherings in Italy, the European country worst hit by the pandemic, are due to expire on March 25.
School closures and other measures, such as a ban fan attendance at sporting events, are due to run on until April 3.
"The measures we have taken... must be extended beyond their original deadline," Conte told Thursday's edition of the Corriere della Sera newspaper.
Carabinieri guard the red zone of Casalpusterlengo in northern Italy
Conte referred to the closures of many businesses, "individual activities" and the shutdown of schools.
A woman wearing a face mask walks across the Campo dei Fiori market square on March 16
The pandemic killed 475 people in Italy between Tuesday and Wednesday, the worst toll in a country in a single day, according to an official count published Wednesday.
A total of nearly 3,500 people have died because of the virus in Italy, more thanin China, where the pandemic began in late December.