Dorsey retweeted the message from @TwitterSupport, providing a bit more information about the decision.
"Verification was meant to authenticate identity & voice but it is interpreted as an endorsement", Twitter's user support division wrote in a tweet on Thursday.
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Twitter claim, however, that the blue tick is too often seen as an endorsement of a verified account by Twitter or as an indication of the account-holder's importance. Chief executive Jack Dorsey said Twitter should have communicated its doubts about the verification system to users faster, and that the network had realized it needed to overhaul its verification process "some time ago". "And we failed by not doing anything about it".
A few years back, Twitter began placing a blue check-mark next to accounts whose users' identities had been verified - a way to help distinguish legitimate accounts from bogus ones. Verifications have been "paused" until the company can resolve the "confusion".
Kessler is remembered for helping organize the white nationalist protest in Charlottesville in August, which led to a woman's death. "I must be the only working class white advocate with that distinction".
Across the Twitterverse, people including comedian Michael Ian Black came down on the company. Though Twitter has suspended several high-profile accounts associated with the alt-right movement, some white supremacist accounts are still active, including Richard Spencer's verified account.
In what appeared to be a response to that overflowing of anger, Twitter said it "paused all general verifications".
A Twitter spokeswoman said that any further updates would be tweeted from the Twitter Safety account.
More recently, an applications process was opened up by which accounts could state why they might justify verification, expanding massively the range of people who could potentially be verified.
Top Twitter officials weighed in on the Kessler decision Thursday from their personal accounts.
Twitter has long grappled with questions and controversy about speech on its platform.