Portugal would have been on May 21-24 while the Italian round in Sardinia was scheduled for June 4-7.
Three rounds of the championship have taken place so far with Argentina postponed.
Portugal last week declared a state of emergency to stem the spread of the virus while Italy, which has seen more fatalities than any other country, is in lockdown.
The next race on the calendar after Italy is Kenya's Safari Rally on July 16-19 but the East African country has cancelled flights and barred entry to people from countries affected by the outbreak.
"All parties will work to identify potential alternative dates for the postponed rallies later in the season should the COVID-19 situation improve," said WRC Promoter managing director Oliver Ciesla in a statement.
He said this would also depend on championship logistics, the ability of competitors to travel and the country's ability to host the event.
Six times world champion Frenchman Sebastien Ogier leads Toyota team mate Elfyn Evans of Wales by eight points in the championship. (Reporting by Alan Baldwin, editing by Ken Ferris)