SAN FRANCISCO – Apple Inc. Chief Executive Officer Steve Jobs says the company knew that the iPhone 4 can lose reception when held a certain way and didn’t think it would be a big issue. He offered customers a case to fix the flaw.

Jobs apologized to users affected by the glitch, which he called “Antennagate,” saying Apple is “working our butts off” to correct it. Most smartphones have the same shortcoming as the iPhone 4, he said Friday at the company’s headquarters in Cupertino, Calif.

Apple, the world’s biggest technology company by market value, aims to burnish the iPhone’s image after Consumer Reports opted not to recommend the device, blaming the antenna glitch. The iPhone accounts for about 40 percent of revenue, making it a bigger moneymaker than the Macintosh or iPod.

The company scheduled the event after users complained about losing signal strength when they held the lower-left corner of the phone.

“We care about all of our users, and we won’t stop until every one of them is happy,” Jobs said. “This is blown so out of proportion, that this is incredible.”

Every iPhone 4 buyer will get a free rubberized case called a Bumper, and people who already bought the $29 accessory will get a refund, Jobs said. Customers can return their iPhone 4 for a full refund within 30 days if they’re still unsatisfied. That’s “everything we can do,” he said.

Bloomberg reported this week that an Apple engineer warned Jobs last year that the antenna might interfere with calls, citing a person with knowledge of the matter. Jobs said Friday he didn’t know about the antenna concerns early on. He called the article a “total crock.”

“We are human,” he said. “And we make mistakes sometimes. But we find out pretty fast and we work to make our customers happy.”

The Bumper giveaway lasts until Sept. 30, when Apple will revisit the policy. The company may have a better idea of what to do about the phone then, Jobs said.

“People don’t see this as a long-term problem,” said Kenneth Schapiro, president of Condor Capital Management in Martinsville, N.J., whose biggest holding is Apple. “They’re seeing it as something the company is going to solve.”