Customers who have already bought a bumper -- a plastic cover that prevents human contact from disrupting the antenna signal -- will qualify for a refund.
Job's announcement came at a much-anticipated press conference at Apple's headquarters in Cupertino, California, called to address a recent flurry of bad publicity over iPhone 4 reception issues. More than 3 million iPhones have been sold to date, he said.
"We're not perfect, and phones aren't perfect either," Jobs said, pacing on stage with an iPhone on hand, wearing his trademark black turtleneck sweater. "But we want to make all of our users happy... and if you don't know that about Apple, you don't know Apple."
Jobs told users they could return their iPhones and get their money back under the company's regular policy.
"If you're still not happy, we'll give full refunds," he said.
Jobs was doing damage control just three weeks after Apple launched the device to great fanfare. More than 1.7 million iPhone 4s were sold around the world within three days, making it the company's most successful launch ever. At the time, Jobs touted it as the "biggest leap" yet from the original iPhone.
But tech reviewers and users soon began complaining about dropped calls and spotty reception when the user's palm covers the bottom left corner of the phone. The flaw, dubbed the "death grip" by bloggers, appears to cut calls off when one's hand interferes with the antenna, which is embedded in the phone's metal shell.
Consumer Reports -- which announced Monday that it could not recommend the iPhone 4, issued a brief statement after Jobs' news conference:
"Consumer Reports believes Apple's offer of free cases is a good first step. However, Apple has indicated that this is not a long-term solution, it has guaranteed the offer only through September 30th, and has not extended it unequivocally to customers who bought cases from third-party vendors," it said. "
We look forward to a long-term fix from Apple. As things currently stand, the iPhone 4 is still not one of our recommended models."
Jobs did not apologize for the defect. Instead, he showed video of other smartphones -- from Blackberry, Droid and Samsung -- that lose signal strength when held in the "death grip."
"We love making our users happy," said Jobs, boasting that the iPhone 4 continues to garner positive reviews from customers and tech experts. "People seem to like it. More important, users seem to want it."
Jobs argued that "antennagate," as Apple has humourously dubbed the issue, is overblown, since just 0.5 percent of iPhone 4 users have called AppleCare to complain, and fewer than 2 percent have returned their phones.
"All smartphones seem to do that," Jobs said of the reception problem that occurs when one's hand covers the antenna. "We haven't figured out a way around the laws of physics."
Nevertheless, Jobs admitted that "we screwed up the algorithm" on the signal strength indicator. "We've been working our butts off" to understand the issue, he said.
Later, during a brief question-and-answer session, Jobs denied reports that he knew about the flaw before the phone was released.
"That's a crock," he said, according to Engadget.com." If anyone had said this thing has problems, we would have dispatched people to deal with that issue."
Nevertheless, Jobs admitted that the iPhone 4 drops slightly more calls than the previous version.
The conference comes after weeks of negative publicity, which Apple until now only addressed with formal statements. When complaints surfaced initially, the company released a statement saying that "gripping any phone will result in some attenuation of its antenna performance, depending on the placement of the antennas."
The company later released another statement, repeating its claim that gripping any phone in certain ways could reduce reception. Apple also said there was a problem with the bars that display signal strength and said it would release a free software update soon to fix the problem.
"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," the company said. "Our formula, in many instances, mistakenly displays 2 more bars than it should for a given signal strength."
At today's conference, Jobs admitted that Apple had "screwed up the algorithm" on the signal strength indicator. "We've been working our butts off" to understand the issue, he said.
Apple's statements did little to satisfy customers, and several lawsuits seeking class action status have been filed.
The backlash reached its peak on Monday, when Consumer Reports said it would not recommend the new phone, though it still ranked it among the world's top smartphones. Then, on Wednesday, Bloomberg News reported that a senior antenna engineer at Apple had warned Jobs early on that the iPhone 4's design could lead to dropped calls.
The Apple press conference seemed to go over well with investors.
When the conference started, Apple stock was trading at $249, and it jumped to a high of $254.97 while Jobs was speaking. (The overall stock market, meanwhile, dropped more than two percent.)
Ross Rubin, analyst at NPD group, said Jobs seemed earnest in his effort to make things right in customers' eyes.
"This clearly represents a good faith effort to address the concerns," he said. "It's not a perfect solution, but there may not be a perfect solution, in that there are inherent tradeoffs in handset design."
Others, however, were not convinced.
"I think it was a mistake to compare this problem to other phones' problems," said Rob Enderle, a consultant and president of the Enderle Group. By not apologizing, Jobs has exposed himself to further criticism and possible retaliaton from other phone companies.
"Saying 'I'm a crook, but hey, so is everybody else,' doesn't usually work,'" said Enderle.
ABC's Ned Potter, Bill Weir and Chris Marderosian contributed to this story.