Congress needs to move on from repealing the Affordable Care Act, says Aetna CEO Mark Bertolini.

"The ACA cannot be repealed, period, end of sentence," Bertolini told CNBC's "Closing Bell" on Thursday.

"What we should do is fix it. So either everyone gets their heads together over in the Senate and the House and does the job that the American people needs them to do, and fix what we already have, or they should move on to something else," he said.

"It's really easy to fix this if they would just get over the politics of who is going to win the '18 election."

For Aetna to rejoin the Obamacare markets, Bertolini says, the system needs to become more stabilized.

"Any business that has the kind of changes this program has seen quarter over quarter, sometimes monthly, would not be able to sustain their business practices for any period of time," Bertolini said. "So when they get it right — which, it can be fixed, it very much can be fixed — and it's stable, we'll reconsider participation."

Late in July, President Donald Trump tweeted that if a new health-care bill failed to pass, "bailouts" — referring to the payments the government needs to make to prevent premiums rising even more next year — for insurance companies could end very soon.

Trump tweet

However, Bertolini challenged what Trump called "bailouts."

"They aren't bailouts," Bertolini said. "We don't keep that money. It goes directly to providers and directly to pay for premiums for members, so I think it's misinformed."

"Our premiums are the same regardless, and it's the costs that need to be paid to hospitals and doctors that otherwise wouldn't be paid," he said. "[The] only people who get hurt are the members and the citizens of the United States who won't get health care as a result, so these aren't bailouts for the insurance company."

The Aetna CEO also fired back at those who say going to a single-payer system is a solution, which he said has failed in Vermont and Colorado.

"If we had the time, I'd take you through the logic of why single-payer, ill-defined, doesn't generate any savings for the American public," Bertolini said.

"There are no single-payer systems in the version that we think we want to create in this country. ... We need to talk about the costs of health care, and getting those costs under control, and that doesn't happen by changing who pays the bills."

Aetna, which reported a second-quarter beat, is up more than 27 percent year to date.