 Some Xbox Live gamers have complained about fraud |
The company admitted it had been forced to make "an unacceptable number of repairs" to the consoles after key hardware failed.
Customers who suffer the problems will now be given a free three-year warranty, the company said.
The failures are indicated by three red flashing lights on the console.
Microsoft, has not revealed how many of its machines have suffered the problem, but said the number was "bigger than we are comfortable with."
It added that the move - which will also see some people reimbursed for postage and repairs on consoles which were out of warranty - was aimed at keeping the loyalty of its customers.
"The majority of Xbox 360 owners are having a great experience with their console and have from day one," said Robbie Bach, president of Microsoft's Entertainment & Devices Division.
"But this problem has caused frustration for some of our customers and for that, we sincerely apologise."
It added its Xbox division was still expected to make a profit during the financial year beginning 1 July 2007.
Migration manoeuvre
Separately the company has announced an October launch of its advanced version of the Xbox - the Xbox 360 Elite - in Japan, where it lags behind Nintendo and Sony in the console market.
And the company has also unveiled plans to open a software development centre in Canada which it said was a way of hiring talented people from abroad who would struggle to obtain a US working visa.
The Vancouver location would "allow the company to continue to recruit and retain highly skilled people affected by the immigration issues in the US", Microsoft said.