A controversial firmware change made earlier this month meant HP printer owners using unofficial, usually cheaper, cartridges discovered they would no longer work.
A campaign calling on HP to reverse the move was launched, backed by rights group the Electronic Frontier Foundation (EFF).
In a blog post, HP admitted it should have done a "better job of communicating” the change.
An optional update that removes the restriction on unofficial cartridges will be available “within two weeks”.
The firm added: “We are committed to transparency in all of our communications and when we fall short, we call ourselves out."
But while making the apology for how it informed users, HP defended the move, saying it did so to protect users from counterfeit products.
"When ink cartridges are cloned or counterfeited, the customer is exposed to quality and potential security risks, compromising the printing experience,” wrote Jon Flaxman, the company’s chief operating officer.
However, campaigners argued HP’s motivation was less about security, and more about protecting the large profit margins it adds to official ink cartridges.
As consumers took to online forums and social networks to express anger, the EFF came down hard, saying HP had betrayed the public's trust.
"Customers should be able to buy an HP printer without fear that the company will later place artificial limits on the printer’s use,” the group said.
"It would be a security nightmare for customers to avoid installing security updates for fear of unwanted and unannounced feature changes."
It also called on HP to explain how it planned to tell customers who may have been affected about the revised update.
"Right now,” the EFF said, “the vast majority of people who use the affected printers likely do not know why their printers lost functionality, nor do they know that it’s possible to restore it.
"All of those customers should be able to use their printers free of artificial restrictions, not just the relatively few who have been closely following this story."
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HP has backtracked on a software update that blocked some ink cartridges made by third parties.