His statement also cut little mustard with United States conservatives, who accused him of obfuscation and of applying different standards to Mr Trump than to rival leaders such as Iran's supreme leader.
US President Donald Trump addresses supporters during a campaign rally at MBS International Airport in Freeland, Michigan on 10 September 2020.
Mr Dorsey has said he believes those measures can promote more fruitful, or "healthy", conversations online and lessen the impact of bad behaviour.
His comments alluded to Twitter's rationale for banning Trump last week, which cited "the risk of further incitement of violence". Although claiming this was the "right decision for Twitter", Dorsey admits it sets a unsafe precedent. Questions about the role that social media platforms - large ones like Twitter, Facebook, Instagram, Snap, and Reddit as well as fringe upstarts like Parler, Gab, and MeWe - played in radicalizing, connecting, inciting, and abetting extremists has come into sharp focus following last week's violence at the US Capitol.More news: When To Expect Cyberpunk 2077’s Free PS5 and Xbox Series X Upgrade
Smaller fringe social networks such as Parler and Gab, both popular with Mr Trump's more extreme supporters, have also been cut off from the mainstream internet over claims that they have allowed their users to call for and organise violence without outcome.
Dorsey also said Twitter itself needed to shoulder some of the responsibility for promoting what he called "healthy conversation", and said it was time to reflect on the company's operations, as well as the environment social media is operating in today.
Dorsey went on to express concern over the actions of Amazon, Apple and Google, which took Twitter competitor offline over the weekend after it became a haven for Trump supporters.
In another tweet, Trump said he will not be attending Biden's inauguration on January 20 which is customary for a U.S. president.
Twitter's decision to permanently suspend Trump is considered overdue by critics who argue he has gotten away with abuses, but has inflamed members of the far right who say it stifles free speech.More news: Veronika Kudermetova upsets Elina Svitolina in three-set thriller — WTA Abu Dhabi
"Last week we announced an indefinite suspension of president Trump's Snapchat account", the platform told AFP.
Dorsey concluded with, "It's important that we acknowledge this is a time of great uncertainty and struggle for so many around the world".
The actions by social media companies angered ardent defenders of Trump, who was impeached by the House of Representatives on Wednesday for inciting "insurrection". He wrote, "This moment in time might call for this dynamic, but over the long term it will be destructive to the noble goal and ideals of the open internet".
Incoming US President-elect Joe Biden has said he wants companies like Facebook and Twitter to do more to take down hate speech and fake news.
The Twitter CEO said bans by social media companies on Mr Trump after last week's violence were emboldened by each other's actions even though they were not co-ordinated.More news: COVID-19 vaccinations top 60,000 in B.C., more on the way
That ban has also been done in the interests of "public safety", the company said.