Telegram, which says it does not bow to "government censorship," has become increasingly popular with activists and protesters.
Germany should order the messaging programme Telegram removed from Apple's and Google's app stores if it continues to ignore requests to help track down extremist content, a senior German official said on Tuesday.
Telegram has been blamed in Germany for fuelling an increasingly virulent subculture of anti-vaccine conspiracy theorists who exchange news about supposed dangers and arrange protests that have spilled over into violence.
The app, which says it does not bow to "government censorship", has become increasingly popular with activists and protesters, especially as platforms like Facebook become more responsive to government pressure to crack down on those spreading lies, threats or conspiracy theories.
Telegram did not immediately respond to a request for comment.
Last month, a group of protesters held a torch-lit gathering outside the home of the regional interior minister of Saxony, in what was widely seen as an implicit threat of violence against her.
"What's happening in Telegram groups and channels violates the compliance rules of Apple and Google who offer it in their stores," Boris Pistorius, regional interior minister of Lower Saxony, told Der Spiegel.
"We must urgently talk to them and persuade them to stop distributing Telegram," he added.
Germany has some of the world's strictest compliance rules for social media networks, obliging them to respond rapidly to reports of extremist content.
But Telegram, which according to its own website was founded in St. Petersburg and is now based in Dubai, has not responded to requests for assistance from Germany's justice ministry for help in tracking authors of extremist content.
The app, which presents itself as a libertarian alternative to other messengers and social networks, has also acquired a devoted following among opposition activists in authoritarian countries such as Belarus and Russia, who value its seeming ability to sidestep state censorship.