Twitter is failing to protect users from cyberbullying and trolls, the social network's CEO Dick Costolo admits.

Costolo made the comment in a leaked memo obtained by the technology and culture website The Verge, accepting responsibility for Twitter's failure to shield its users from online harassment.

"We suck at dealing with abuse and trolls on the platform and we've sucked at it for years," he writes in the memo. "It's no secret and the rest of the world talks about it every day. We lose core user after core user by not addressing simple trolling issues that they face every day."

Costolo's remarks came amid several high-profile incidences in which Twitter users, primarily women and girls, abandoned the social media network, citing a torrent of vitriol aimed at them from other community members.

'Ashamed' by tolerance of abuse

Among those who quit in recent months was British mother Sara Payne, who endured years of online trolling after her daughter was murdered in 2000. Comedian Robin Williams's daughter, Zelda, left Twitter and Instagram after being inundated with abusive words about her father following his suicide.

Writer Lindy West recently confronted her cruellest troll, interviewing him on the radio show This American Life.

Costolo said he was "ashamed" that Twitter continues to allow people to be subjected to vicious attacks, and vowed in a followup email to "fix" the problem.

"It's nobody else's fault but mine, and it's embarrassing," he wrote, adding that it was time to begin "kicking people off right and left" for abusing other members.

Twitter released new tools in December in a bid to make the Twitter experience safer by introducing a new way to flag abusive tweets. It also rolled out improvements to how its "blocked" accounts page would work.

In 2013, Twitter U.K. apologized after several high-profile users spoke out about receiving rape and death threats. The company added staff to deal with trolling complaints and added a "report abuse" button across all mobile platforms and its desktop website.