An initial public offering (IPO) "is not something we're focused on right now," Costolo said in an interview with the financial network CNBC.
"There will come a time when we need to start talking about what's the best way to finance the future growth of the company and then we'll have that conversation."
Costolo said the disastrous IPOs of other social media firms like Facebook, whose stock has fallen as much as 50 percent since May, is not a factor in considering whether or when to go public.
"Nothing external to the company has had any bearing on how I think about when to take Twitter a public company or not to," he said.
Asked whether Twitter might be sold to another firm, Costolo commented: "We have every belief that we are going to be an independent company, and that we've got the engine that we need to be a successful independent company."
He said the company is executing its strategy of getting revenues from the mobile space.
"Our mobile ads are going pretty well," he said, adding that the ads begun earlier this year have produced days where revenue from mobile exceeds non-mobile revenues.
Twitter, which allows its members to post brief comments, links or pictures, claims to have more than 140 million active users, with the largest number being in the United States.
A recent survey found one in seven Americans who go online use Twitter and eight percent do so every day.
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