Apple Inc. 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 Officer Steve Jobs announced the giveaway today during a news conference at the company’s headquarters, even as the company denied that the iPhone 4 has an antenna problem that needs fixing. The more than 3 million people who have already bought the iPhone 4 and new buyers through Sept. 30 will all be eligible.

People who already purchased the $29 “Bumper” cases will be refunded.

Jobs began the event by saying, “We’re not perfect,” but was quick to point out that no cell phone is perfect. He played a video showing competing smart phones, including a BlackBerry from Research in Motion Ltd., losing signal strength when held in certain ways.

Phones usually have an antenna inside the body. 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 of the phone, but means that 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.

Today, 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 more than five out of every thousand users have complained to Apple’s warranty service, and less than 2 percent 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.”