The head of the third-biggest U.S. health insurer said he has "serious concerns" about whether or not Obamacare's new markets are sustainable, echoing criticism from other top for-profit insurers.

"We continue to have serious concerns about the sustainability of the public exchanges," Aetna Inc. Chief Executive Officer Mark Bertolini said on a call Monday while discussing the company's fourth-quarter results. "We remain concerned about the overall stability of the risk pool."

Large U.S. health insurers have faced a rocky start in the Patient Protection and Affordable Care Act, which in 2014 opened up new markets where millions of Americans buy coverage, often with tax subsidies to help them afford it. Aetna is one of the biggest insurers in Obamacare and, like its rivals UnitedHealth Group Inc. and Anthem Inc., has struggled to make a profit in the business.

Aetna's 1 million individual commercial members make up 4.3 percent of its total membership, as of Dec. 31. Of those, 750,000 are people who signed up through the exchanges. The insurer expects total membership to remain roughly flat this year. Pretax operating losses from the individual business were about 3 percent to 4 percent last year, though should improve this year, Aetna Chief Financial Officer Shawn Guertin said Monday.

Taking Losses

UnitedHealth has said that it will probably take about $1 billion in losses on Obamacare plans when 2015 and 2016 results are combined. The company has that it should have stayed out of the market longer, and that it may quit the program in 2017.