Fixing the verification system is one of the steps Twitter says it's taking to tackle hate speech, abuse and misinformation on the social media service.
Verification, which awards blue check marks to confirm the identity of a Twitter user, was suspended last year after the social media service came under fire for verifying white supremacist Jason Kessler, who used Twitter to organise rallies such as Unite the Right's torch-wielding march in Charlottesville.
Twitter originally began verifying accounts to distinguish individuals in public life — celebrities, politicians, journalists and others — from impersonators.
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Anyone can apply to be verified on Twitter, yet the decision-making process is opaque. Twitter says blue check marks are not intended to be an endorsement but they have become status symbols that confer perks such as appearing at the top of searches.
"The main problem is we use it to mean identity, but because of the way it was originally started, where it was only given to certain very large public figures, celebrities, etc., it came to have a lot of status associated with it, as well," said David Gasca, one of Twitter's product directors, on the Periscope livestream.
"They think of it as credibility. Twitter stands behind this person. Twitter believes that ... what they're saying is great and authentic, which is not at all what we mean by the check mark."
Twitter has verified the accounts of some of the students from Marjory Stoneman Douglas High School, who have spoken out on gun control after a shooter killed 17 people.
Dorsey said Twitter would be more open about decisions it makes in the wake of accusations of bias and censorship from conservatives.
"We have a lot of work ahead, it's not going to be overnight. We're going to be as open as we can," he said. "That's going to be uncomfortable for us in many ways, but we want to be very open and very vulnerable with you all about what we're facing and what our challenges are."