For Mr. Murdoch, buying the 61 percent of Sky that Fox does not currently own would give his company full control of a strongly performing business to which the media mogul has a special attachment. He founded the broadcaster in the early 1990s and had previously tried to buy the entire company, only to be forced to withdraw his bid in the wake of a British phone-hacking scandal involving one of his tabloids.

Comcast’s move, telegraphed two months ago, seizes upon Fox’s troubles in getting government approval for its bid. British regulators have questioned whether buying Sky, which operates the 24-hour news channel Sky News, would give Mr. Murdoch too much control over the country’s news media, given his ownership of newspapers like The Times of London and The Sun.

It also changes the calculus for Fox and Disney. Both have already offered concessions to allay regulators’ concerns, including an offer to sell Sky News to Disney.

But now they may be forced to pay up to win Sky.

Under the terms of its offer, Comcast would pay 12.50 pounds, or $17.45, a share in cash for each Sky share. Fox has offered £10.75 a share.

Hoping to press on Fox’s weak spot, Comcast said that it was committed to Sky News’s editorial independence, offering to set up a board for the news unit and maintain its funding. Comcast also repeated pledges to increase investment in Britain’s film and television industries.