Apple will give free protective cases to buyers of its latest iPhone to alleviate the so-called "death grip" problem in which holding the phone with a bare hand can muffle the wireless signal.

Apple chief executive Steve Jobs announced the giveaway on Friday during a news conference at its headquarters, even as the company denied the iPhone 4 has an antenna problem that needs fixing.

The more than 3 million people who have bought the iPhone 4 and new buyers through September 30 will all be eligible.

Apple CEO Steve Jobs appears on stage during a news conference at Apple headquarters in Cupertino, California, to address the issue of the iPhone 4's reception issues.

People who purchased the USD 29 "Bumper" cases will be refunded.

Jobs began the event by saying, "We're not perfect," but was quick to point out no mobile phone is perfect. He played a video showing competing smartphones, including a BlackBerry from Research in Motion, losing signal strength when held in certain ways.

In designing the iPhone 4, Apple took a gamble on a new design, using parts of the phone's outer casing as the antenna. That saved space inside the tightly packed body, but means covering a spot on the lower left edge of the case blocks wireless signal.

Consumer Reports magazine said covering the spot with a case or even a piece of duct tape alleviates the problem. It refused to give the iPhone 4 its "recommended" stamp of approval for this reason, and it had called on Apple on Monday to compensate buyers.

On Friday, in the company's first remarks following the magazine's report, Jobs said Apple was "stunned and upset and embarrassed".

Jobs said the iPhone 4's antenna issue isn't widespread. He said just over five out of every thousand users have complained to Apple's warranty service, and less than 2 per cent have returned the device.

"We're not feeling right now that we have a giant problem we need to fix," Jobs said. "This has been blown so out of proportion that it's incredible. I know it's fun to have a story, but it's less fun when you're on the other end of it."

Analysts have criticised Apple's first responses to reports of reception problems as dismissive.

Jobs apologised to buyers who had less than perfect experiences.

"We're going to do whatever it takes to make them happy and if we can't make them happy we're going to give them a full refund and say we're really sorry we inconvenienced you, and we're going to do better next time."

The refund applies even for those who have long-term contracts with AT&T Inc., the iPhone's exclusive US wireless carrier.

Jobs, a cancer survivor, also addressed a question about his health on Friday.

"I'm doing fine. I was even better earlier in the week (when) I was having a vacation in Hawaii, but I decided this was important enough to come back for," he said. "I'm doing great."

AP