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Apple has said sorry to iPhone customers whose phones were disabled after third-party repairs, and issued a fix for the problem.

Some users found that their iPhone stopped working following servicing by a non-Apple technician and saw an "error 53" message in iTunes.

Previously, Apple had said the error was a "security measure" taken to prevent fraudulent transactions.

Now, the company has released a software update to fix the error.

In a statement, Apple said that "error 53" occurs when a device fails a standard security test designed to ensure that the Touch ID fingerprint scanner is working correctly.

However, the company added: "We apologise for any inconvenience, this was designed to be a factory test and was not intended to affect customers.

"Customers who paid for an out-of-warranty replacement of their device based on this issue should contact AppleCare about a reimbursement."

A software update has now been released so that iPhone customers with disabled phones may restore their device via iTunes on a PC or Mac.

"To me, there was a lot of logic in what they said around the 'error 53' element," said mobile analyst Ben Wood at CCS Insight.

"If you're using your fingerprint to unlock sensitive data or make payments and there was the ability for someone to replace the screen and modify the module to take control of your phone - that's not a good thing at all."

Mr Wood added that Apple faced something of a backlash over the error after it appeared "retrospectively" on repaired phones following a software update, and was not something iPhone users had expected.

Apple had even faced a class action lawsuit led by a Seattle-based firm over error 53-disabled phones.

"I think it's a sensible decision by Apple," he told the ´óÏó´«Ã½.

"If they've found a way to allow people to do repairs to the phone without that error occurring, that's great news."

Some customers praised the company's decision on .

"Perhaps my sentiment of a week ago or so (that I would not buy an iPhone 6), which generated so much complaining by people with huge numbers of posts, in its small way helped to prod Apple into fixing this," wrote one user, risandy, following news of the fix.

"Glad to see Apple have back-tracked on this one," added Jay 75.