The decision by the company, behind Universal and NBC in the US, clears the way for the only other bidder for the US entertainment assets owned by Fox, Disney, to proceed with its $71bn offer unchallenged.
Fox had accepted that bid.
It now leaves Fox battling Comcast for control of Sky.
Comcast is leading the way in the bids for the UK entertainment firm – posting an improved £14.75 per-share offer last week.
That trumped a bid made just hours earlier by Fox of £14-per share for the 61% of Sky that it does not already own.
Both offers have been recommended to Sky shareholders by Sky’s independent directors.
Comcast said on Thursday: “Comcast does not intend to pursue further the acquisition of the 21st Century Fox assets and, instead, will focus on our recommended offer for Sky.”
Chief executive, Brian Roberts, added: “I’d like to congratulate Bob Iger (Disney counterpart) and the team at Disney and commend the Murdoch family and Fox for creating such a desirable and respected company.”