Some of these users who have accused Twitter of discriminating against the marginalised claimed that they have already created Mastodon accounts for saner conversations.
"I have mentioned my #Mastodon account here. If you have a Mastodon account please follow me. Let's get out of this toxic Twitter," said one user.
"Because @TwitterIndia is suppressing dissent, selectively suspending liberal accounts, throttling the reach while taking no action against those who are spreading hate/violence, many folks have migrated to #Mastodon," wrote another user.
As rumours about Congress leaders Rahul Gandhi and Priyanka Gandhi opening accounts on Mastodon also circulated on social media, the party came out with a tweet to put speculation to rest.
"This is to clarify that the accounts of Shri @RahulGandhi, Smt. @priyankagandhi or that of INC India on Social Media platform, Mastodon are not authentic," the official Twitter account of the Congress party said on Friday.
Mastodon allows users to do many things that one can do on Twitter - publish posts and follow others. But compared to Twitter's over 300 million users, it has just about 2.2 million users.
But getting into this decentralised and open source network is not as easy as opening a Twitter account.
Created by Eugen Rochko, who is now 26 years old, Mastodon is made up of many servers and all of them can have their own rules.
As Rochko explained in an interview to web and podcast network magazine Slate last year, Mastodon is a "federated platform" - a collection of servers and websites.
"Centralisation is not just centralisation of power, but centralisation of data as well. So the more data a platform like Facebook collects it's all in one place. It's easy to access and to analyse," Rochko was quoted as saying.
"With Mastodon, the data is separated. Every server stores only the data of its local signed-up users and the data that they subscribe to from their friends. If you take the data just from one server, you don't have a lot," Rochko added.
The interest in Mastodon increased in India after Twitter found itself in the midst of a controversy surrounding its rules.
The row started after the accounts of a number of Twitter users, including the account of senior lawyer Sanjay Hegde, were suspended or curtailed.
Apart from Hegde, senior columnist Dilip C. Mandal got briefly restricted. But Mandal continued the tirade against Twitter. As others joined him, a flurry of tweets followed under #CasteistTwitter, #JaiBhimTwitter and #cancelallBlueTicksinIndia over the course of this week.
Twitter India on Thursday said that it is an impartial platform and does not take action based upon any ideology or political viewpoint.
"There's been a lot of discussion this week about Twitter's perceived bias in India. To be clear, whether it's the development of policies, product features, or enforcement of our rules, we are impartial and do not take action based upon any ideology or political viewpoint," Twitter India said.
( With inputs from IANS )