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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The Dow Jones rose 0.2% to 19,251.78, while the wider S&P 500 gained 0.3% to 2,204.71, just missing a new record. The  Nasdaq rose 0.5% to 5,333.00.
Banking shares performed strongly, with Wells Fargo up 2.2%, Bank of America rising 1.5% and Goldman up by 1.2%.
Financial shares have climbed by over 15% since the election.
President-elect Donald Trump's plans to reduce corporate tax and regulations are expected to benefit the sector.
Meanwhile, analysts are predicting the Federal Reserve will raise interest rates next week, in another boost for banks.
Financials in general are "benefiting from the feeling that interest rates are done going down and we are going to see a much more favourable interest rate and spread environment for financials," said Paul Nolte, portfolio manager at Kingsview Asset Management.
Mr Trump's announcement that Japanese telecoms and internet firm SoftBank had agreed to invest $50bn in the US also boosted markets, with Sprint shares rising 1.5%and T-Mobile gaining 1.8%.
Other telecom stocks also rose.
AT&T shares increased by 1.9% after the firm said its new streaming television service DirectTV Now has gained more subscribers so far than expected.
Verizon shares climbed 1.2 % after the wireless carrier said it was selling 29 data centres for $3.6bn.
Chipotle was one of the top fallers on the S&P 500, dropping 7.6%, after it said sales had not recovered as well as expected.
Quarterly sales have been falling over the past year since food safety issues led to the temporary closure of dozens of Chipotle restaurants across the US.
HP has backtracked on a software update that blocked some ink cartridges made by third parties.
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(Close) The Dow Jones Industrial Average closed at a fresh high for a second consecutive day after a rally in financial shares boosted the index.