The South Korean company expects sales of the flagship handset, which was released last month, to hit ten million next month. This makes it the fastest-selling Samsung product of all time.

The enthusiasm for the phone has taken the company by surprise. US networks, including Sprint, T-Mobile and AT&T, have not been able to stock the top-end version, and Samsung executives acknowledged: “Supply simply cannot meet soaring demand.”

The squeeze is the result of an inability to source more of its key components, and Samsung has dispatched executives to its suppliers to get production back on track. It said that it expected an improvement from next week and that it foresaw a strong performance in the second quarter as a result of the booming sales.

Estimates of Samsung’s performance have been lower in recent weeks over concerns that competition from the likes of Huawei and ZTE, the Chinese suppliers, could hit volumes at the lower end of the market.

Shares in Samsung Electronics fell by 4.2 per cent in Seoul after the company’s update on the progress of the Galaxy S III.

The success of the Galaxy range has triggered fears that the mobile sector industry has become a two-horse race because sales of products from Nokia, Research In Motion, which makes BlackBerrys, and HTC have withered.

Samsung expects to sell 200 million smartphones this year, having become the world’s largest developer of mobile phones with computer-like functions.

Samsung, which sold 21,000 phones an hour in the first three months of the year, according to analysts, accounts for half the sales of phones built on the Android operating system developed by Google. The Galaxy S III has a larger screen than the latest iPhone and incorporates functions such as voice recognition.

Apple has been told by a judge in the United States that it cannot pursue an injunction to block the sale of Motorola Mobility devices because of accusations of patent infringement. Apple had not clearly shown that its phones had lost market share or brand recognition as a result of the alleged infringement by the Google-owned Motorola, Judge Richard Posner said in dismissing the case.