The stakes now stand at 26 billion pounds ($34 billion) - the value of Comcast's latest offer. That bid came after Fox raised its bid to 24.5 billion pounds ($32.5 billion) earlier in the day.
Comcast's new bid translates to 14.75 pounds per share, or 18 percent more than its original offer. Fox is dangling 14 pounds per share for the 61 percent of Sky that it doesn't already own, more than 30 percent above its first bid in December 2016.
The duel for Sky is unfolding as Fox itself is the object of a takeover battle between Comcast and Disney. Disney said in June it is offering more than $71 billion for Fox's entertainment businesses in a counterbid to Comcast's nearly $66 billion offer.
Sky operates in Austria, Germany, Ireland and Italy as well as the U.K. It has 22.5 million customers, attracted by offerings such as English Premier League soccer and "Game of Thrones."
Fox, which is run by media mogul Rupert Murdoch, still faces significant regulatory battles in Britain. The challenges include the culture secretary's assertion that Fox would have to sell Sky News to win government approval because of concerns about media plurality.
Fox's bid for Sky is the most recent episode in Murdoch's long-running effort to take full control of the company.
His last bid foundered amid a 2011 phone-hacking scandal, in which journalists working for Murdoch newspapers were accused of gaining illegal access to the voicemail messages of crime victims, celebrities and members of the royal family. News Corp., which is controlled by the Murdochs, withdrew its bid for Sky soon after.
Both Comcast and Fox want Sky in order to amass more programming as they compete for viewers with both traditional TV networks and technology companies such as Netflix and Amazon.
AP Business Writer Michael Liedtke in San Francisco contributed to this story.
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