Comcast Corp. dropped its bid for 21st Century Fox’s entertainment assets amid mounting odds, clearing the way for rival Walt Disney Co. to acquire key pieces of Rupert Murdoch’s media empire for $71.3 billion.

However, Comcast said it was still pursuing European pay-television giant Sky PLC, which also has been the subject of a takeover battle between Comcast and Fox. Comcast has the higher offer for the operator, in which Fox already owns a 39% stake. Disney Chief Executive Robert Iger has called Sky a “crown jewel” in the...