The Affordable Care Act—also known as Obamacare—is "not an affordable product" for many people and it does not fix the underlying problems causing high health-care costs, Aetna Chairman and CEO Mark Bertolini told CNBC on Wednesday.

"If we're going to fix health care, we've got to get at the delivery of care and the cost of care," Bertolini said in a "Squawk Box" interview. "The ACA does none of that. The only person who's really going to drive that is the consumer and the decisions they make."

"Getting everybody insured should probably be our goal, but you have to have a more affordable system," he added. "We have a 1950[-style] health care system in the Unites States."

Aetna said Tuesday that its more than estimates in the second quarter, due in part to the higher costs of covering patients who bought insurance under Obamacare for the first time. But the third-largest U.S. health insurer also reported better-than-expected earnings and revenue in the second quarter and raised full-year guidance.

"We have more people in the system using health care. So if you have coverage you are going to use it, particularly if you haven't had coverage before and have pent-up demand," the Aetna CEO explained. "Usually utilization and health care [also] pick up as the economy recovers, people get back to work and they get more coverage."

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But Aetna expects medical spending this year to be at the low end of its forecasts and said the second quarter does not represent a new upswing after years of slowing growth in health costs.