"We need to pick sectors that can restart their activity. If scientists confirm it, we might begin to relax some measures already by the end of this month," Conte told the British broadcaster.
Conte warned, however, that Italy could not lower its guard and restrictions would only be eased gradually.
There were 542 deaths from COVID-19 in Italy on Wednesday, lower than the 604 the day before, taking the total death toll to 17,669. There were 3,693 people in intensive care, down from 3,792 on Tuesday – the fifth daily decline in a row.
The decline has raised hopes the virus is on the retreat thanks to a nationwide lockdown, though the number of new cases rose 3,836, compared with 3,039 on Tuesday, to reach 139,422, the third highest globally behind the United States and Spain.
Italy imposed the nationwide lockdown on March 9. Two weeks later, Conte announced that non-essential businesses, including car, clothing and furniture manufacturing, would have to close.
Businesses in the country's northern industrial heartland have been urging the government to let them reopen factories to prevent an economic catastrophe, even though the north is the area worst hit by the coronavirus.
Branches of employers lobby group Confindustria representing the northern regions of Lombardy, Veneto, Piedmont and Emilia-Romagna, which account for 45% of Italy's economic output, called on the government on Wednesday to set out a "roadmap" for a return to work.