In this file photo, Alex Jones from Infowars.com speaks during a rally in support of Republican presidential candidate Donald Trump near the Republican National Convention in Cleveland, Ohio, July 18, 2016.
With a series of bans and content removal by major technology firms, Jones has complained that there is a coordinated "big tech" agenda to silence him.
"If we succumb and simply react to outside pressure, rather than straightforward principals we enforce (and evolve) impartially regardless of political viewpoints, we become a service that's constructed by our personal views that can swing in any direction".
Senator Murphy rejected the criticism, arguing that restrictions on free speech by companies could not be compared to government censorship and that the case of Jones - who is a controversial figure standing accused of endorsing conspiracy theories and bullying - would not lead to more cases of online censorship of popular voices.
Apple has removed the entire library for five of Infowars' six podcasts from its iTunes and Podcast apps, BuzzFeed News has learned.
It also noted that some of the content banned from other platforms hasn't shown up on Twitter.
Dorsey also appeared to put the onus of identifying false information on individual users, calling on journalists to "document, validate, and refute such information".
Dorsey went on to explain that the company would "hold Jones to the same standard we hold to every account".
"We've been banned completely on Facebook, Apple and Spotify", Jones tweeted on Monday.
Jones, who has 858,000 followers on Twitter, has built up his profile while promulgating conspiracy theories.