Apple sold about 500,000 iPhones on the gadget’s debut weekend, according to analysts, as one of the most-hyped product launches delivered an estimated $275 million (£137 million) in sales.

However, many new iPhone users found themselves battling with technical glitches that left them unable to activate their new gadgets.

ATT, the only mobile phone company to offer the iPhone after signing an exclusive deal with Apple, admitted demand had stretched its system, affecting "a small number" of users.

An Apple website attracted hundreds of complaints. "It has now been 48 hours and my iPhone is still the prettiest paperweight I own," one purchaser wrote.

The iPhone is rendered useless without a connection - not even the gadget's alarm clock will work.

A characteristically secretive Apple is yet to comment on the iPhone’s early performance after the weekend launch. It had previously set a target of sales of ten million over the next 12 months — equating to about 1 per cent of the mobile phone market.

Piper Jaffray and Global Equities Research put the number of sales of the device at 500,000 and 525,000 respectively.

However, after a strong start, the real test for the gadget now begins.

Analysts believe that the device will redefine the mobile market, not least by putting what is billed as a full-blown internet browser into consumers' pockets for the first time.

But they have also been quick to identify the troubling "iPhone paradox" — that the cutting-edge handset will run on ATT’s relatively slow Edge network and not a faster 3G system.

On the plus side for the new device, analysts list its “PC-like” software that will be pitched against clunky traditional phone systems, Apple’s design prowess and the near unprecedented level of publicity that the group stirred up.

Aside from its reliance on ATT’s "last generation" Edge network — which will not allow iPhones to download large files such as music tracks — other possible downside factors include a high initial price ($499 for a 4-gigabyte model and $599 for an 8-gigabyte version) and a probable lack of interest from corporate clients — a key market for smartphone rivals such as the BlackBerry.

Shares in Apple have gained about 50 per cent since the iPhone was announced in January valuing the group at about $106 billion.

Times Recommends

• Minister in talks with Saudis to protect creditors
• Premier Inn hits back in £29-a-room row
• Bankers hit back at 'populist' bonus supertax