Australia and Denmark intend to roll out apps within two weeks, while Jens Spahn, Germany's health minister, has confirmed that its app will be ready to download in three to four weeks' time.
Australian prime minister Scott Morrison told Triple M radio: "I will be calling on Australians to do it, frankly, as a matter of national service.
"This would be something they might not normally do in an ordinary time, but this is not an ordinary time. If you download this app, you'll be helping to save someone's life."
Meanwhile, Microsoft recently pledged to provide security tools to healthcare organisations around the world.
The tech giant announced that AccountGuard will be free to healthcare, human rights, and humanitarian groups amid a spike in attacks during the coronavirus pandemic.
A Microsoft spokesperson explained: "Every patient deserves the best possible healthcare treatment, and we all need to thank and applaud the truly heroic work by those risking their own health to help those who are sick.
"Their work is challenging enough but is being made more difficult by cyber-attacks, now or in the future."
Amnesty International, Freedom House, and Human Rights Watch have already taken up the offer, according to Microsoft.