"We lose core user after core user by not addressing simple trolling issues that they face every day,” he said. "I'm frankly ashamed of how poorly we've dealt with this issue during my tenure as CEO. It's absurd."
In a follow-up message, Costolo made it clear that he takes "personal responsibility" for the prevalence of abuse on the network.
He added that the site was going to "start kicking these people off right and left and making sure that when they issue their ridiculous attacks, nobody hears them."
Twitter has for long admitted it has not done enough to stop trolling and online abuse.
Last year in December it had released an update, which included features intended to reduce online abuse. It improved the blocking function, which allows users to stop others from contacting them, and made its harassment reporting tools quicker and easier to use.
When it introduced those, Twitter admitted in a blog post that it had not done enough to protect its users.
"We are nowhere near being done making changes in this area," wrote Shreyas Doshi, director of product management and user safety at the site.
In the coming months the site would release "additional user controls, further improvements to reporting and new enforcement procedures for abusive accounts," he added.
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