Apple says a fault on its new iPhone 4 is causing it to incorrectly display the phone's signal.
Users who gripped the phone - which went on sale on 24 June - on the lower left-hand side noticed the signal strength and reception fell away.
Apple says the problem relates to an error on how the signal bars are displayed, rather than the signal.
However, some industry experts say that there may be a deeper signal problem than a cosmetic design flaw.
Apple is promising a patch fix "within a few weeks". Users may also choose to get a full refund within 30 days of purchase, the firm has said.
In a statement, Apple said the iPhone 4 had been "the most successful product launch in Apple's history" and that all phones gripped in "certain ways will reduce its reception by one or more bars".
"We have discovered the cause of this dramatic drop in bars, and it is both simple and surprising," the statement read.
"Upon investigation, we were stunned to find that the formula we use to calculate how many bars of signal strength to display is totally wrong.
"Our formula, in many instances, mistakenly displays two more bars than it should for a given signal strength. For example, we sometimes display four bars when we should be displaying as few as two bars.
"Users observing a drop of several bars when they grip their iPhone in a certain way are most likely in an area with very weak signal strength, but they don't know it because we are erroneously displaying four or five bars.
"Their big drop in bars is because their high bars were never real in the first place."
Apple said it was going to adopt AT&T's formula for calculating how many bars to display for a given signal strength.
The theory now is that, once the patch update has been applied, iPhone's bars will report signal strength "far more accurately" providing users a better indication of the reception in a given area.
But Stuart Miles, editor of technology site Pocket Lint, was sceptical.
Speaking to BBC News, Mr Miles said the news raised a few questions.
"Why, for the first time, has Apple released a bumper for their phone, and why does no one else have this problem," he asked.
"HTC makes metal phones, but they seem to work just fine.
"Changing the display may make some people feel better, but it doesn't really fix the problem," he added.
Apple said the new software to fix this would be released in a few weeks, claiming that as the problem also existed in the original iPhone, it would also be available for the iPhone 3GS and iPhone 3G.
However, there have been few - if any - complaints about older iPhones losing signal strength when held in a certain way.
Apple's previous advice for iPhone 4 owners to overcome the problem of the device losing signal was to not place your hand on the lower left corner.
Apple chief executive Steve Jobs said: "Just avoid holding it in that way."
This latest approach is an unusual admission from the company, which has apologised for "any anxiety we may have caused".
The iPhone 4 went on sale on in June, with hundreds of people queuing Apple's flagship stores across the globe.
Many new owners reported that signal strength dropped when the phone was held.
The casing of Apple's latest phone is made of stainless steel, and also serves as its antenna.
The problem is thought to be particularly acute for left-handed owners who naturally touch the phone in the sensitive area.
Apple sells a rubber "bumper" that shields the sensitive area, as do many other firms.
When Mr Jobs introduced the iPhone 4 at Apple Worldwide Developers Conference, he described the integrated antenna as "really cool engineering".