Telegram detailed the attack in a colourful thread on Twitter, explaining to users that the issue could disrupt the service but would not compromise personal user data.
Telegram did not reveal more about the attack's origin.
"We're now experiencing a powerful DDoS attack, Telegram users in the Americas and some users from other countries may experience connection issues".
Durov added that historical attacks of the same size had coincided with protests in Hong Kong, adding, "This case was not an exception".
Police and protesters had pitched battles in the city on Wednesday over plans to allow suspects to be extradited to mainland China.
The botnet sent so much useless traffic to Telegram servers that they could no longer handle the requests from legitimate users, leading to unstable connections. Yesterday, the service went down after it was affected by a "powerful" DDoS attack for roughly an hour.
"IP addresses coming mostly from China".
China's Foreign Ministry and cyberspace administration did not immediately respond to AFP's requests for comment.
It also supports encrypted voice calls.
Encrypted messaging apps like Telegram and WhatsApp are preferred around the world by a wide variety of people trying to avoid surveillance by the authorities - from Islamic State in Iraq and Syria (ISIS) terrorists and drug dealers to human rights activists and journalists.
Other apps have faced blocks in China as well during political movements in Hong Kong.
People are anxious that should the extradition bill pass, it would bring Hong Kong more decisively under China's control.