But some users saw Apple’s revelation as vindication of their longstanding belief that the company had been purposely slowing down old iPhones to get them to buy new ones.

In its statement on Thursday, Apple denied that it had ever — or would ever — “do anything to intentionally shorten the life of any Apple product, or degrade the user experience to drive customer upgrades.”

Still, Apple apologized for what it called a “misunderstanding” and promised it would cut the price of out-of-warranty iPhone battery replacements to $29 from $79 for anyone with an iPhone 6 or later model beginning in late January; the company said the service would be available worldwide through December 2018.

Apple also said it would soon issue a software update with new features that would allow users to more clearly see the health of their iPhone’s battery.

“We know that some of you feel Apple has let you down,” the company said. “We apologize.”

In Thursday’s statement, Apple took pains to clarify what it had apparently been trying to convey last week: that rechargeable batteries become less effective as they age; that an aged battery under the duress of a heavy workload can cause a device to shut down unexpectedly; and that the company had released a software update about a year ago “that improves power management during peak workloads to avoid unexpected shutdowns.”