Fox, which owns 39 percent of Sky and is due to gain British regulatory clearance for the deal this week, upped its offer to 14 pounds per share, from its earlier 10.75 pounds per share.
Comcast's initial offer was considerably higher than the Fox bid that valued the satellite broadcaster at £18.5bn.
Fox has increased its bid by just over 30% since its first offer in December 2016.
According to The Hollywood Reporter, an executive for 20th Century Fox has filed a lawsuit to put a stop to the sale of 21st Century Fox's studio assets to Disney, which he claims violates securities rules. Comcast offered $65 billion and is getting ready for yet another bid for Fox. A letter sent to employees by Lachlan and James Murdoch seemed to suggest they expect the deal with Disney to close within six to 12 months following the Department of Justice's conditional approval.
The then Culture Secretary, Matt Hancock, said last month there would be no public interest concerns with a Comcast takeover of Sky.
The new offer has the backing of Sky's independent committee of directors, which withdrew its support for Fox's previous bid after Comcast made its approach. Comcast has until the end of this week to make a new offer.
The skirmish for control of Sky is being fought in the shadow of an even bigger battle - a struggle for control of prized entertainment assets owned by Fox, including its stake in Sky.
Rupert Murdoch's Fox has been waiting for approval from United Kingdom regulators before putting the deal to shareholders.
"They're way behind the curve still", said Crispin Odey, founder of Odey Asset Management LLP, which owns shares of Sky. Analysts said it was not a knock-out, and Fox did not say it was its final offer.
"There are enough sub-plots in the race to acquire Sky to commission a primetime drama", Salmon said.