Several online civil rights groups, including the Center for Democracy and Technology and the San Francisco-based Electronic Frontier Foundation, have questioned the power of tech giants and cautioned those who cheer corporate take-downs of far-right users and Nazi websites that they could be next.
Mr Dorsey said the site had "mistakenly pointed to the wrong reason" the videos remained online, with the company adding its current media policy had not been violated, but would "continue to re-evaluate and examine our policies as the world around us evolves".
Twitter has always been accused of amplifying the reach of people and rhetoric that promote hate, extremist views and violence. But for years, Twitter billed itself as the "free speech wing of the free speech party", exerting little control over its legions of anonymous users.
Twitter says it will now begin enforcing the new rules it announced last month to combat abuse and hateful conduct, including threats of violence and physical harm.
Twitter said it will also allow some hateful imagery and hate symbols in tweets, but users will be warned that it's sensitive content.
"If an account's profile information includes a violent threat or multiple slurs, epithets, racist or sexist tropes, incites fear, or reduces someone to less than human, it will be permanently suspended", Twitter's safety team explained in a company blog post Monday.
As a private company, Twitter has the legal right to block any speech it wants, since the First Amendment only applies to government control of speech.
But even then it can be hard to tell whether a company is implementing its rules fairly or singling out certain people or groups that it may not like, Llansó said.
One account that was no longer visible on Twitter was that Britain First leader Jayda Fransen, whose anti-Islam messages were retweeted by Trump, and another leader of the group, Paul Golding. Twitter has also been criticized for the seemingly arbitrary way it enforces its rules and has previously said it plans to do a better job of responding to users' reports of abuse.
In addition to Golding and Fransen, the BBC reports that American Nazi Party, the Traditionalist Working Party and other neo-Nazi or alt-right accounts have been suspended for failing to comply with Twitter's new policy.
The company declined to specify what others or how many were removed.
This isn't the first time Twitter has targeted white nationalists and other leaders associated with the far-right.