European football's governing body and tournament organisers UEFA will hold a video-conference on Tuesday to discuss domestic and competitions across the continent, as well as Euro 2020, which is due to take place from June 12 to July 12.
Italy are set to host the opening match in Rome on June 12, in a tournament which will be played in 12 countries across Europe.
"We will ask for an act of responsibility from UEFA and all the continental federations," Gravina told Italian radio.
"First of all for a path that aims to protect the health of athletes and fans from all over the world, even if the epicentre of the pandemic is now in Europe.
"I hope that tomorrow common sense proposals will come out. Postponement is the way forward right now."
All sport in Italy has been suspended until April 3 with the country in lockdown to avoid the spread of the virus which has killed 1,809 people and infected more than 24,000.
The FIGC confirmed its federal council, scheduled for March 23, had been postponed.
"We are sailing in unchartered waters in a climate of absolute fog," added Gravina.
"Taking into account the advanced level of club competitions we must first facilitate the conclusion of the championships and cups.
"And we must not overlook the idea of completing international competitions, Champions and Europa League."
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