Outside of China, Italy has been the hardest hit by the virus – named COVID-19 – with more than 1,400 deaths recorded from at least 21,100 cases.
The global pandemic has forced the postponement of all sport, including Serie A, until April 3 in Italy, where the country is in lockdown with all shops except food stores and pharmacies closing.
“Please stay home and respect the rules,” Conte said in a video message posted via Inter’s official channels.
“That’s the only way to confront this emergency.
“It’s a difficult and tough moment but if we stick together, we’ll get through it. Don’t give up!”
Rugani was the first Serie A player to test positive for COVID-19, which has spread alarmingly quickly in the country, while Manolo Gabbiadini is among a number of Sampdoria players to contract the virus.
Juventus beat Inter 2-0 at the Allianz Stadium on March 8 in a behind closed doors fixture, which ensured that the reigning Italian champions remain on course to retain their crown.
The Bianconeri are top of the Serie A standings by a single point ahead of Lazio after 26 fixtures, with Inter now nine points off the pace in third.
It is not yet known when the 2019-20 campaign will resume, with a number of major European leagues now thought to be considering the complete cancellation of the season as efforts to contain the spread of coronavirus continue.