* Murdoch seeking to win UK approval to take control of Sky
* Says will legally separate Sky News or sell it to Disney
* Some lawmakers oppose increase in Murdoch's influence
* Sky shares rise 2 pct (Adds shareholder, CMA comments, updates shares)
LONDON, April 3 (Reuters) - Rupert Murdoch ratcheted up the pressure on Britain to approve his $15 billion-plus bid for pay-TV group Sky by offering to sell or legally separate Sky News, aiming to head off objections the deal could give him too much political influence.
Murdoch's Twenty-First Century Fox said on Tuesday that Walt Disney Co was interested in buying Sky News. Alternatively, Fox said, Sky News could be legally separated within the Sky group.
Even if Fox's proposals satisfy Britain's government and competition regulator, however, it may still need to raise its recommended offer for Sky after U.S. cable group Comcast Corp said it intended to make a higher counter-bid.
At 1350 GMT, Sky shares were up 2 percent at 13.24 pounds, the biggest rise on Britain's FTSE-100 index and above both Fox's bid and Comcast's proposed offer, signaling investors expect any suitor will have to pay more.
Loss-making Sky News is the last regulatory hurdle in 87-year-old Murdoch's long campaign to buy Sky, which has grown from its UK beginnings to become Europe's biggest pay-TV group.
"We look forward to concluding this acquisition - finally - in a timely and expeditious manner," Fox senior vice president Gerson Zweifach said, adding the proposed solutions addressed all concerns about the transaction.
Fox agreed in December 2016 to buy the 61 percent of Sky it does not already own, but the deal has been repeatedly delayed by the UK government and regulators, allowing Comcast to gate crash the deal in February.
Fox had already promised that Sky's 24-hour news service would remain independent under the ultimate control of Murdoch, but critics, including some high-profile politicians, remain adamantly opposed due to Murdoch's record of influence through owning the Sun and the Times newspapers.
As the Sky deal remained in regulatory limbo, Fox separately agreed to sell a string of assets, including its 39 percent stake in Sky, to Disney, potentially taking Murdoch out of the Sky equation.
Some Sky shareholders, frustrated by the delay, had already said Fox should increase its 10.75 pounds-a-share offer.
Their view appeared vindicated when Comcast said it would pay 12.50 pounds a share to buy Sky, although it has not yet made a formal bid.
Fox said its new concessions went beyond the steps that Britain's media regulator Ofcom said would mitigate concerns about Murdoch's influence.
The company, however, needs to persuade another regulator, the Competition and Markets Authority (CMA), and the government.
A CMA spokeswoman said on Tuesday it had until May 1 to provide its report on the proposed deal to Britain's minister for digital matters, culture, media and sport. The minister, Matt Hancock, is due to make the final decision by June 13.
Fox said it could sell Sky News to Disney, or legally separate Sky News within the wider Sky group, so it would operate independently with guaranteed funding for 15 years.
One London-based hedge fund said the measures should be sufficient, but that "the price issue is not going away," suggesting Fox would have to raise its bid.
Analysts at Liberum said two factors pointed to Fox coming back with a revised bid to match Comcast.
First, Fox must have received approval from Disney to offer the concession, they said, and second, Sky said its independent directors remained focused on maximizing value for shareholders.
Separate news on Tuesday that Sky Italia had settled its long-running fight with Mediaset in the Italian pay-TV market also made Sky more valuable, they added.
A group of high-profile British lawmakers, including former Labour party leader Ed Miliband, called last month for Murdoch to be blocked from buying Sky, despite the promises Fox had already made to ensure the independence of Sky News.
The four said the promises did not go far enough, given Murdoch's record of influence.
Fox said on Tuesday a group of politicians was seeking to influence the CMA, adding they were making "a number of unsupported and fanciful assertions."
($1 = 0.7120 pounds) (Additional reporting by Maya Keidan; Editing by Guy Faulconbridge and Mark Potter)