"Verification was meant to authenticate identity and voice but it is interpreted as an endorsement or importance", the company said on Twitter.
Kessler had deleted his account previously after insulting the late Heyer's appearance and linking to extreme neo-Nazi website The Daily Stormer.
Given the furore over Kessler's blue tick, it's worth asking how a white supremacist can end up getting verified in the first place.
Twitter on Friday said that it has paused all general verifications while they work on resolving it.
Originally, verification was applied entirely manually by the Twitter team, with verified status simply appearing without warning for those accounts that might qualify.
Milo Yiannopoulos, former contributor for the right-wing site Breitbart, was also verified and then "un-verified" by Twitter, according to Vanity Fair, before he was permanently banned from the site. The platform verifies accounts across a range of fields-from sports people like Cristiano Ronaldo, to politicians like President Donald Trump, to religious figures like Pope Francis-but says that the account must be in the public interest to warrant verification. It has also increased the characters for the Twitter display name. In other words, if you're not newsworthy by Twitter's standards, you may be denied verification. Rather, the goal of verification is to simply confirm that the account holder is who they say they are.
Twitter's official support account confirmed that its verification system had been "paused" following the backlash. For critics of Twitter's ongoing failure to effectively address the harassment that occurs on its platform, the move was viewed as yet another example that the social network is not taking the appropriate actions to police its platform.