The ban came weeks after Apple, Alphabet's YouTube, and Facebook took down podcasts and channels, citing community standards.
Trump's comments in an interview with Reuters come as the social media industry faces mounting scrutiny from Congress to police foreign propaganda.
An app belonging to popular conspiracy theorist Alex Jones remains in the company's mobile App Store because it has not been found to be in violation of any content policies.
Dorsey said Twitter reasoned it was journalists' job to shine the light of truth on unsubstantiated rumours or sensationalised issues.
Facebook said it removed four pages belonging to Jones for repeatedly posting content in recent days that break community standards on hate speech, bullying and glorifying violence.
Apple told Buzzfeed that it has removed the entire library for five of Jones's six Infowars podcasts including the shows "War Room" and the daily "The Alex Jones Show".
Infowars posted a statement on its website in which it said YouTube had slapped the Jones channel with a "community strike," meaning he cannot broadcast live on YouTube for 90 days.
At the forefront were websites known for relaying bogus theories, including the notion that the shooting at Sandy Hook Elementary School was a hoax.