Prime Minister Giuseppe Conte said curbs would be eased from 4 May, with people being allowed to visit their relatives in small numbers, in masks.
Parks will reopen, but schools will not restart classes until September.
Italy has reported 26,644 virus-related deaths, Europe's highest official toll.
The country recorded 260 new deaths on Sunday, the lowest daily figure since 14 March. It has confirmed 197,675 cases of the virus, according to data from Johns Hopkins University, which is tracking the disease globally.