Explaining the timing of that decision, Dorsey said it came down to keeping business running smoothly.
"We did not want to interrupt that momentum, if anything we want to amplify it because we're extremely excited about the products and new initiatives to come," Dorsey said. He explained that this momentum can be seen in new products like Periscope.
Despite Dorsey's insistence to the contrary, many maintain that Twitter is in need of a big shift—and that change may need to come to its board.
"We're seeing the consequences of poor governance here...Twitter is rapidly becoming the BlackBerry of social media," Harvard Business School's Bill George said.
Discussion among analysts and some in the media has turned to whether Twitter could potential be sold to a larger tech firm. Costolo, however, said Friday that the board is not looking for a sale.
"Jack and I and the rest of the board all know that we have a fiduciary duty to our shareholders to maximize value, and we think we can do that best as an independent company," he said, declining to comment on "the existence or non-existence" on any conversations with other firms.
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Dorsey, who also leads financial services company Square, will be splitting his time between the two firms. Some sources have suggested to CNBC that Dorsey will be in contention for taking the permanent Twitter chief position, but he told CNBC that's not a priority for him at the moment.
"It's not even a question I'm considering right now," he said, responding to a second question about whether he would take the CEO job by saying he's "not focused on it."
Still, not everyone is convinced that Dorsey would make a good permanent CEO for the company.
"I can understand putting [Dorsey] in that seat for a time so they can take their time and make a good decision," said Kevin Landis, Firsthand Capital Management's CEO and CIO. "The way he answered that question about whether he would take that job permanently, I think there were reasons for why he stepped down from that job the first time, and those reasons are probably still valid."
—CNBC's Jacob Pramuk and David Faber contributed to this report.