Microsoft has apologised after sporadic problems affected Xbox Live gamers over the Christmas period.

The company has promised a free Xbox Live Arcade Game to all members for their "loyalty during this holiday period".

Marc Whitten, general manager of Xbox Live, posted an open letter on the official Xbox website explaining that a "massive increase in usage" caused "intermittent Xbox Live issues over the holiday break".

"During this holiday season you helped us break a number of Xbox Live records. This included our largest sign-up of new members our five year history and the single biggest day of concurrent members ever on the service," he wrote.

Although the service was never completely offline, many users experienced repeated problems, including issues with signing in, matchmaking and account recovery.

"We are disappointed in our performance. I would like to take this moment to thank you all for your patience and understanding as our team has worked around the clock to return the service to a stable state," Whitten wrote.

"As a thank you for your loyalty during this holiday period, we will be offering all of our Xbox Live members around the world access to a full Xbox Live Arcade game free of charge."