CUPERTINO, Calif. — Apple CEO Steve Jobs took the stage at his company’s Cupertino headquarters Friday to respond to complaints about the new iPhone 4.

Jobs said the company will give a free bumper case to buyers of every iPhone 4 through Sept. 30.

Apple will tap cases made by third-party providers because Jobs said the company can’t make enough. Users will be able to order them online starting next week. “Pick a case — zoom, we’ll send it off to you,” Job said.

Earlier, Jobs said, “You know, we’re not perfect. Phones aren’t perfect. We want to make all our users happy.”

Calling the situation “Antennagate,” Jobs said the company has been “working our butts off” the past 22 days to figure out what the underlying problem is.

He also pointed out the that other smart phones, like the BlackBerry Bold, have similar “death grip” problems like that on the iPhone 4, with some owners reporting dropped calls when they touch the antenna at the lower left corner of the device.

He began the presentation with a defense of the iPhone 4 while admitting “we are not perfect.”

Showing a video of other smart phones being held as signal strength drops, he said: “Most smart phones behave exactly the same way. This is life in the smart phone world — phones are not perfect. And it’s a challenge for the whole industry. Every phone has weak spots.”

Jobs detailed the $100 million of research the company put behind antenna research. “We knew if you grip it a certain way, the bars would go down — just like every smart phone. We didn’t think it would be a problem.”

He said very few users have complained about the iPhone 4 antenna.

About “one-half of one percent — 0.55 percent” have called the company’s Apple Care service for help regarding this issue. “Historically for us, this is not a large number. This does not jibe with what you read about this.” He also said there have been less than a third of the returns for the iPhone 4 than for the previous model, the iPhone 3GS.

The event followed a Monday review by Consumer Reports that, while declaring the iPhone 4 the best smart phone on the market, recommended that readers not buy it because of the reception problem.