Italy had to serve as a model of how to fight it, hit hard by the virus weeks before other major Western countries. He is closely monitored worldwide as he takes his early steps to track a path from a rigorous lockdown imposed by him in early March.
Conte described a phased process in which much production would restart at the beginning of May, even though the general public, such as bars and restaurants, would have to wait a little longer. Until September, schools would remain shut.
"In those hours, we are working to allow a good deal of enterprises to be reopened from production to construction for May 4," said Conte in the Italian daily La Repubblica.
Some companies considered "strategic," including export-oriented activities, could open again this week provided they were able to get ahead with local prefects.
Exporting companies need to resume their activity quickly so that the risk of losing business is reduced and cut out of the production chain, he said.
"We can't extend this lockdown any longer ... We risk seriously undermining the country's socio-economic fabric, "said Conte.
Conte reiterated that any restart must be gradual, and said that companies must introduce strict safeguards before they open their doors.
The newspapers said that industries with a low risk of contagion, such as manufacturing and wholesale companies, would be permitted to open on May 4. On May 11, retailers and bars and restaurants were able to reopen on May 18 under tough conditions.
The lockdown has placed strain on the third largest economy in the euro zone and Italian managers have called for limitations that can easily prevent economic catastrophe.
Rome has introduced a number of measures to help businesses remain afloat, including government-supported loans. However, some businessmen have complained about delays.
Conte said that the government monitors banks to ensure that state-guaranteed liquidity reaches businesses.
He said the government was also working on a range of measures to help industry reduce bureaucratic bureaucracy.
When asked about schools, Conte said in September the plan was to reopen them. But the risk of contagion was very high, he added. Remote teaching works well, he said.