Apple last night responded to the row over low reception on its new iPhone by promising everyone who has bought one a free rubber case to fix the problem.

Since the company launched the iPhone4 on 7 June, some users have complained that the signal strength collapses when they grip the device over its built-in antenna, a new feature of the phone.

Apple had resisted giving away free cases but after the influential US magazine Consumer Reports warned its customers not to buy the phone and Apple's share price dropped, the company called an emergency press conference at its headquarters in Cupertino, California.

Chief executive Steve Jobs held out an olive branch to customers. "You know, we're not perfect," he said. "We know, you know.

"And phones are not perfect either. But we want to make all of our users happy ... We love making users happy."

Apple said anyone who wanted one could apply on its website from Thursday for a free "bumper" – a rubber case – or a refund if they were still unhappy.

Defending the US giant's reputation, Mr Jobs claimed that many smartphones experience sudden falls in reception when held in a certain way and demonstrated the problem with a Blackberry Bold smartphone.

"It's certainly not unique to the iPhone4," he said, adding that pictures of the fault on rival handsets were available on YouTube.

Only 0.5 per cent of Apple iPhone customers had complained to the company about "antennagate", he added, but conceded that tests showed more calls cut out on the device than its predecessor.

His conciliatory tone demonstrated a change in the company's attitude towards the problem. In an email to customers two weeks ago, the firm indicated the low reception stemmed from a software fault that exaggerated the signal rather than a fault with the handset itself.

Two days later, The Independent on Sunday printed Apple's private advice to staff not to give free bumpers, which were selling for £25, to consumers. It told its AppleCare helpline staff: "We ARE NOT appeasing customers with free bumpers – DON'T promise a free bumper to customers."

Upon the iPhone 4's launch last month, Mr Jobs hailed it as the "biggest leap" since the launch of the iPhone in 2007.

A quarter slimmer than its forerunner, the phone has a camera on the front for video calls, greater movement sensors and a glass and steel case. However it was dogged with complaints about reception, particularly when users held it over its built-in antenna.

Consumer Reports, which publishes guides on everything from cars to TVs, said that it had also tested other phones – including the iPhone 3GS – and found none had the signal-loss problems of Apple's iPhone4.

Prior to the press conference, analysts said Apple needed to take quick action to avert any lasting damage to its reputation. "They need to provide an actual fix – not a bumper fix – so the product performs as it should," said Ashok Kumar at Rodman & Renshaw.

"Apple should have taken a higher road when addressing the design flaw, instead of taking the hard-line stance."

After the conference, Fraser Macdonald, editor of gadget magazine Stuff, told Sky News: "Apple has come up with some plain speaking, saying, 'OK, we'll give you a free case but if that doesn't work, we will give you a full refund'."