Comcast, which owns NBC and Universal Pictures, said it was offering 12.50 pounds per share, significantly higher than the 10.75 pounds per share agreed by Fox.
The proposed offer pits Comcast against Murdoch, who helped to launch Sky in Britain, and also against Walt Disney which has agreed to buy a string of assets from Fox once the deal is done, including Sky.
“We would like to own the whole of Sky and we will be looking to acquire over 50% of the Sky shares,” Comcast CEO Brian L Roberts said in a statement.
21st Century Fox agreed to buy the 61% of Sky it did not already own in December 2016 but the takeover has been repeatedly held up by regulatory concerns that Murdoch controls too much media in Britain.
Some Sky shareholders have also started to complain that the offer was too low.