Fox said it would establish a fully independent board for the news channel to ensure the 86-year-old media mogul and his family could not influence its output.
Britain's competition regulator said last month that Fox's deal to buy the 61 percent of Sky it does not already own should be blocked unless a way was found to reduce the influence Murdoch could wield through owning the Sun and the Times newspapers, as well as TV, radio and online news outlets.
Some lawyers, investors and analysts have said that a stronger mechanism to guarantee the independence of Sky News should be enough to gain approval.
Looming over the Fox-Sky takeover is a $52.4 billion deal that would result in Walt Disney Co buying Fox's TV and film studios, its cable TV assets and international TV businesses including Sky - leaving the Murdochs with Fox's U.S news and sports channels, as well as their News Corp newspaper and publishing assets.
The Competition and Markets Authority (CMA) had already said the Disney deal should be taken into consideration when any remedies are assessed.
Fox, which disputes the CMA's finding on the media power it would have if it owned Sky, said any concerns about the Murdoch influence would fall away after a Disney takeover.
The regulator had said the output of Murdoch's companies would be watched, read or heard by nearly a third of the British population, giving him too much sway over public opinion.
In January it put forward three broad possible solutions: insulating Sky News from Fox's influence, spinning off or divesting Sky News, or blocking the deal outright.
Sky, however, warned the regulator that if it blocked the deal, it could close the loss-making channel completely, killing the main British competitor to the BBC in 24-hour TV news.
Fox said the regulator's assessment was based on a number of legal and factual errors, but nonetheless promised to fund Sky News for at least five years and said it would put a "firewall" around the channel as remedies.
"The combined effect of the Proposed Firewall Remedies is that there could be no circumstances in which, post-transaction, the MFT (Murdoch family trust) or members of the Murdoch family could influence, whether directly or indirectly, the editorial line or policy of Sky News," the company said.
It said it would establish a fully independent board to oversee Sky News, including the appointment of the head of the channel, who will have sole responsibility for editorial strategy and staffing.
The proposal builds on a previous Fox pledge to create a Sky News board with a majority of independent directors.
But the CMA noted opponents of the deal had said previous offers by Murdoch to guarantee the editorial independence of the Times newspapers in Britain and the Dow Jones company had proved ineffective.
Former opposition Labour leader Ed Milliband and ex-Conservative finance minister Kenneth Clarke were among four lawmakers who said the deal should be blocked, arguing if the independence of Sky News was lost, it would be difficult or impossible to restore, and that the CMA could reconsider the deal if Disney buys Fox.
Fox's proposals were released by the CMA on Monday. It is due to present media secretary Matt Hancock with a final report by May 1 and he has said he will rule on the deal by June 14.
Shares in Sky were trading up 0.36 percent at 10.53 pounds at 1216 GMT. Fox has offered 10.75 pounds a share.
(Editing by David Evans and David Holmes)
By Paul Sandle