Comcast increased its bid for Sky to $34 billion on Thursday, topping.
The quick counteroffer suggests that the war to seize control of Britain's biggest pay-TV company is heating up, since the previous bid wasin April.
The increased pace of bidding caused Sky shares to rise 3.2 percent in London on Thursday, with investors anticipating further bids, Bloomberg reported.
"Comcast has long admired Sky and believes it is an outstanding company and a great fit with Comcast," Comcast said in statement.
Sky noted that both Comcast and Fox have cleared regulatory pre-conditions in terms of bidding.
Fox already owns 39.14 percent of Sky, but this effort to get a stronger hold on its entertainment assets is an element of Disney's possible.
In the US, Disney has been inwith Comcast -- the nation's largest cable TV provider -- to buy 21st Century Fox's film and TV studios.
Fox owns major franchises including X-Men, Deadpool, Kingsmen and Planet of the Apes. It also owns animated films such as Ice Age, TV shows like The Simpsons and the FX network.
First published July 12 at 3:09 a.m. PT.
Update, 6:40 a.m. PT: Adds comment from Sky and Comcast.