The head of the third-biggest US health insurer said he has ‘‘serious concerns’’ about whether or not the Affordable Care Act’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 chief executive 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 US 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 under the law also known as 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.

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.

In the past, Aetna had been more upbeat. Bertolini said in October that it was ‘‘way too early to call it quits on the ACA and on the ­exchanges,’’ and that the health law offered a ‘‘big opportunity.’’

‘‘We believe we have an obligation to stick it out and work with it until we know that it won’t work,’’ Bertolini said last month. ‘‘It is too early to give up on this process.’’

Guertin echoed those comments Monday. ‘‘I would not say that we’re more pessimistic,’’ he said. ‘‘I would say we’re very much in the same place, which is that it’s premature to declare victory or defeat here.’’

Guertin said Bertolini’s remarks were intended to underscore that, even though Aetna’s ACA business appears to be improving, the company still thinks there changes are needed in the ACA’s markets.

‘‘I don’t want that to get lost in this discussion,’’ he said. ‘‘We do need things in the long haul to be done to make this a stable risk pool and one that can provide affordable coverage to people over time.’’

Earlier Monday, the company reported earnings. Fourth-quarter net income rose 38 percent to $321 million, or 91 cents a share, from $232 million, or 65 cents a share, a year before, the company said in a statement on Monday. Operating earnings were $1.37 a share, compared with the $1.21 average of analysts’ estimates.