Unity Biotechnology wants to create drugs that slow, halt or even in some cases reverse specific diseases of aging, CEO Keith Leonard told CNBC on Thursday.

In fact, he said, the company can "absolutely" do it.

"The evidence is mounting, both in our company and outside, that you can intervene and you can change the course of these specific diseases," Leonard said on "Power Lunch."

The company is targeting a "powerful biology" called cellular senescence, which is the aging of an individual cell and how it affects disease.

There is already a phase one trial underway for osteoarthritis, which Leonard hopes to have the results for during the first quarter of next year, he said.

Other diseases that could eventually be treated include the loss of cardiac and pulmonary function as well as cognitive and vision function — "things we have come to accept as part of the normal course of aging," he said.

In the near future, he anticipates, diseases can be treated as they emerge in patients.

"In the far future, we can imagine a world where you can go into the clinic once or twice a year and have your senescent cells removed and kind of you [are] maintained in a more youthful, vigorous state."

Leonard's comments caused the stock to soar almost 18 percent before trading was halted for volatility. After trading resumed a short time later, Unity Biotech shed some of those gains. It was up about 8 percent in midafternoon trading.

The biotech company, which has a market cap of $916 million, has attracted the attention of tech giants such as Amazon founder Jeff Bezos and PayPal co-founder Peter Thiel. Both have invested in Unity Biotech, which has received more than $300 million in funding, including $85 million raised after going public this past May.

— Andrew Zaleski contributed to this report.