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Twitter's interim CEO Jack Dorsey spoke on CNBC's "Squawk Box" Friday morning to discuss the company's transitions, along with outgoing CEO Dick Costolo. CNBC Screenshot

New, “beautiful” products are coming to Twitter, interim CEO Jack Dorsey told CNBC Friday morning. Outgoing CEO Dick Costolo, who announced Thursday he would be stepping down July 1, and his interim replacement spoke exclusively to CNBC to explain the company’s transition.

"The fundamentals and the primitives that the company is working on right now are really strong and beautiful, and I can't wait for the rest of the world to see it,” Dorsey said.

CNBC asked Dorsey what the company could expect from him as leader for the next six months, to which the co-founder said, “The more the product simplifies, the more the product seems straightforward. The more we ship and execute, the more we will have going forward.”

Dorsey cited the acquisition of live video streaming app Periscope as a step Twitter already has taken to improve its product -- one that has been criticized by Wall Street investors for failing to meet user growth goals. "I think it's an amazing, amazing manifestation of what Twitter's future is,” Dorsey said.

Other product changes could include simplifying the way new users can join Twitter. In the past few months, Twitter has made several changes to improve the experience, such as changing the homepage to make it easier to view and engage with public tweets. But the future may include increasing the pace at which these new product changes are executed.

Costolo will remain on Twitter’s board. Talks on his transition began at the end of last year, but Costolo told CNBC he wanted to ensure that the executive team was strong before he announced his resignation. “We had a good, long three-hour conversation about the state of the team,” Costolo said.

Twitter has organized a search committee to look for the next CEO, and Dorsey himself and other internal contenders have been touted as possibilities. Dorsey spoke highly of Kevin Weil, the senior vice president of product, and Weil’s close relationship with the head of engineering, Alex Roetter.

Dorsey himself declined to elaborate on his consideration for the role. “It's not even a question of considering right now,” said Dorsey, who has to juggle not only leading Twitter but also the payment app Square, where he also serves as CEO.

The bearded, 38-year-old Dorsey did, however, comment on the state of his appearance after CNBC asked if he would consider shaving and if it affected how Wall Street viewed the company. “People shouldn’t be measured by what they look like,” Dorsey said.

Twitter (NYSE: TWTR) stock was initially up 2 percent when the market opened Friday, but fell to 1 percent shortly after the conversation with CNBC ended at 10:20 a.m. EDT.