Aetna Inc. told Justice Department antitrust officials in a letter early last month that if they sued to block its deal to acquire Humana Inc., it would immediately reduce its presence on the Affordable Care Act health-insurance exchanges and cancel a planned expansion.

The public emergence of the bluntly worded letter, from Aetna’s Chief Executive Mark T. Bertolini, has led critics to question the motives behind the insurance company’s recently disclosed pullback from the insurance exchanges. It also has added a layer to...