Xbox Live General Manager Mark Whitten said the problems stemmed from a "massive increase" in new users of the service over the holiday season, when sales of video game hardware and software surge.
"While the service was not completely offline at any given time, we are disappointed in our performance," Whitten said in a statement.
Whitten said all Xbox Live members around the world would be able to freely download one game over the service. Games sold on Xbox Live typically cost from $5 to $20, and Whitten said Microsoft would give details of the offer in the coming weeks.
Before the holiday sales surge, Xbox Live had more than eight million members, many of whom were paying $50 a year for the premium service that lets them play online against others.
Whitten did not give details of the cause of the problems, but gaming Web sites and forums have been filled in recent days with complaints from users frustrated with the inability to sign on to the service or play online.