The Associated Press reported that Fox, which already has a 39 percent stake in Sky, raised its offer to 14 pounds per share ($18.58), more than Comcast's latest offer but not equivalent to the value Sky was trading at on Wednesday.
"We remain committed to the United Kingdom and believe that our offer for Sky will bring the best value for all the company's stakeholders and are delighted that the Independent Board of Sky has recommended our offer to its shareholders".
Fox has been attempting to purchase Sky since December 2016, and has increased its offer by more than 30 percent since then, according to the AP.
Indeed, there is speculation that, should Disney prevail in the fight for Fox, Comcast would redouble its efforts to nab Sky, which would add a valuable worldwide component and new revenue stream to the US cable giant's portfolio.
Sky's shares were up 3 percent at 15.38 pounds on Thursday, valuing it at 26.6 billion pounds, or $35 billion, as investors bet the battle has further to run for a group which owns a slate of top sport and original drama content.
Comcast subsequently made a rival offer of $66bn in cash for those assets - prompting Disney to sweeten its terms last month to $85bn, including debt, in cash and shares.
Murdoch owns major British newspaper titles The Times and The Sun and critics say obtaining full control also of the rolling television channel Sky News would give him too much influence in the news business.
The British government is expected to finally allow Fox, which is run by Rupert's son James, to buy Sky this week, after the USA group agreed to sell Sky's award-winning news channel to Disney to prevent Murdoch from owning too much of the British media. Comcast is said to be ready to negotiate with the feds on the number of Fox RSN's it would have to divest as some of them may overlap with Comcast's NBC Sports regional networks. The opposition has not completely subsided despite the plan to spin off Sky News.