Twitter is also preparing to tackle another issue that has dented its ability to add new users: the trolls.
Costolo said he aims "to make Twitter and all these kinds of platforms a clean, well lit place … without harassment or abuse."
Earlier this week, an internal memo from Costolo was leaked to the media. "We suck at dealing with abuse and trolls on the platform and we've sucked at it for years," the memo read. "We lose core user after core user by not addressing simple trolling issues that they face every day," it said.
Costolo told CNBC that Twitter plans to take action quickly.
"[You want to] change the economic equation around [the abuse] so the onus and burden isn't on the person being abused to report it, but rather the onus and the burden are on people who are engaging in harassment to prove that they should be allowed to continue to use the platform," Costolo told CNBC.
"It should just be taken care of automatically and algorithmically by the platform and we have a number of initiatives underway to make that the case."
Twitter has faced a number of high-profile trolling cases in the recent past. In January, Anita Sarkeesian, a feminist commentator on sexism in video games, recently published a week's worth of messages she received via Twitter, including a large number of obscenity-laden rape and death threats.
Interview by Carl Quintanilla. Julia Boorstin contributed to this article.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1