Restaurants and cafes will operate at 25% capacity and shut at 10 pm from Saturday, while mosques and churches will be open for daily praying but not for end-of-week prayers or services, Mostafa Madbouly said.
Beaches and parks will remain shut and public transport will be suspended from midnight until 4 am.
The decisions to ease restrictions introduced three months ago could be revoked if people do not follow the rules still in place, Madbouly said.
Egypt has seen an acceleration of new coronavirus cases in recent weeks, with infections confirmed by the health ministry surging to 56,809, including 2,278 deaths.
As in other countries, many coronavirus cases are believed to go unreported. The higher education minister cited a study on June 1 estimating that the actual number of cases could be up to five times higher than the reported figure.
The government, which had imposed a night curfew but never a full lockdown, has been trying to limit the economic impact of the virus, telling citizens they will have to learn to live with the pandemic.