Portugal was due to host round five of the 2020 season on May 21-24, while Italy was scheduled for the start of June.
The state of emergency has been extended in Portugal as a result of the COVID-18 epidemic, while Italy continues to be one of the epicenters for the virus.
As a result, both events and the FIA have agreed the postponement of the rallies.
No new dates have been announced yet.
"All parties will work to identify potential alternative dates for the postponed rallies later in the season should the COVID-19 situation improve, taking into consideration championship logistics, the ability of competitors to travel again and the ability of the country in question to prepare and host the WRC at such a time," said WRC promoter managing director Oliver Ciesla.
Rally Mexico took place earlier this month but was cut short by three stages in order to help teams beat travel restrictions.
Winner Sebastien Ogier said afterwards that the rally should not have taken place.