Conte made the announcement on Friday, despite pressure from business unions to begin easing the restrictions.
Conte said Italy could not afford another spike in infections and needed to exercise extra caution in the face of the new disease.
“We are all, I imagine, impatient to get going again,” Conte said in a televised address.
He said the extension of the lockdown for another three weeks was “a difficult but necessary decision for which I assume full political responsibility”.
Conte’s decision followed days of consultations with scientists and union leaders with a range of conflicting concerns.
Conte agreed to allow a tiny fraction of businesses that had been shuttered since March 12 to re-open on a trial basis from Tuesday.
Conte specifically mentioned book stores and baby clothes shops on the grounds that they rarely draw crowds and can more easily impose social distancing measures.
He also said that if the infection rate allows any further easing before May 3, the government would pursue it.
A miscalculation by Conte could, however, result in a new spike in infections or do unnecessary damage to the economy by keeping everything shut for longer than strictly required.
The rest of the world is watching closely to see which way Italy chooses as it seeks to come out of its worst crisis since World War II.
