Rupert Murdoch’s News Corporation offered to buy out minority holders of Fox Entertainment Group Incorporated for $5.86 billion, to solidify control over his largest American asset.

News Corporation, which owns 82% of Fox, said in a statement yesterday that it plans to offer 1.9 Class A shares for each Fox Class A share. That values the bid at about $32.55 a share at yesterday’s closing price. Fox shares yesterday rose to $34.28, about 5.3% above the offer’s value.

Murdoch has boosted News Corporation’s American presence by moving its headquarters to New York from Sydney in November and getting the company’s stock added to the Standard & Poor’s 500 Index. Fox’s assets include the Fox News Channel and 20th Century Fox studio. Mr. Murdoch said in October he would consider buying full ownership of Fox, which produces about 75% of News Corporation’s revenue.

“It’s a cleaner investment scenario for investors, a little easier to understand,” said a JB Hanauer & Company analyst in Hallandale, Fla., David Joyce. He rates both stocks “market perform” and doesn’t own either. “It takes a layer of complexity away.”

Fox shares rose $3.06, or 9.8%, at 4:16 p.m. in New York Stock Exchange composite trading. They’ve increased 18% in the last year. News Corporation’s Class A shares fell 52 cents to $17.13 and have increased 10% in the past year.

Fox shares yesterday topped the pershare value of News Corporation’s offer, suggesting that some investors may expect the company to raise its bid, Mr. Joyce said.

“It’s not a lowball offer, but it’s also not extremely generous,” Mr. Joyce said. “It’s possible that some other outside interest could come in and try to have it forced up, but it’s not probable.”

One reason is that Fox shares are trading at their highest price since they were first sold to the public in 1998, said an analyst at Fulcrum Global Partners LLC in New York, Richard Greenfield. The bid also will be constrained because News Corporation doesn’t have to buy the shares. It already controls the company through its 82% stake, said Mr. Greenfield, who rates Fox shares “neutral” and doesn’t own them.

“Maybe most importantly, the fact is News Corp. is growing faster that Fox,” Mr. Greenfield said. “News Corp.’s currency in our mind is even more undervalued than Fox.”

Parent companies that have bought out minority stakes held by the public have had to increase their initial bids in some cases. Family-owned Cox Enterprises offered $32 a share last August to buy the public’s 38% stake in cable-TV operator Cox Communications.

After public shareholders criticized the bid as too low and Cox Communications shares traded above the offer, Cox Enterprises raised it to $34.75 a share in October. The purchase was completed in December.

Asked on a conference call what it would take to push up News Corporation’s bid for Fox, the chief financial officer, David Devoe, said, “the offer stands.”

Fox shareholders filed six lawsuits in Delaware against both companies and Mr. Murdoch seeking to bar the purchase. Fox directors, including Messrs. Murdoch and the president and chief operating officer of both Fox and News Corporation, PeterChernin, “breached their duty of loyalty” to shareholders by accepting a transaction that is “unconscionable and unfair and grossly inadequate,” shareholder Janice Allen said in a suit filed in Delaware Chancery Court.

Having shares of Fox trade separately provided a means for American investors not permitted to own foreign stocks to buy into the company, Mr. Devoe said.

“Since the reincorporation of News Corp. in the U.S., the logic for Fox no longer exists,” he said. “We really took Fox public as a way to drive value into the stock.”

The combination will save $3 million to $7 million in costs such as legal and auditing expenses, Mr. Devoe said.

Fox Entertainment also owns the Fox broadcast TV network and station group and a 34% interest in DirecTV Group, the largest American satellite-television provider.

Fox generated net income of $1.4 billion, or $1.44 a share, on sales of $12.2 billion in the year ended June 30. News Corporation reported net income of $1.6 billion, or $1.17 a share, on $21 billion in revenue, including its share of Fox.

Management of the Fox assets is the responsibility of Mr. Chernin.

Mr. Murdoch has been giving more power to his sons, Lachlan, 33, and James, 32. Lachlan is deputy chief operating officer of News Corporation, with responsibility for the New York Post newspaper and Fox-owned television stations. James is chief executive of British Sky Broadcasting Group, the Britain-based satellite television service that News Corporation controls through a 35% stake.

News Corporation is benefiting from a strategy of buying just enough stock to control distribution platforms such as DirecTV and BSkyB, Mr. Greenfield said.

“Those assets aren’t generating the same type of cash flow growth as the content and programming assets are,” he said. “There are longer-term risks in the distribution business. News Corp. gets the benefits from distribution, but I don’t think it needs to own more.”

The Fox purchase leaves some questions unanswered. John Malone’s Liberty Media Corporation in December boosted its ownership of News Corporation voting shares to 18% by exercising an option to swap non-voting stock for voting shares. The transaction will be completed by mid-January, Liberty said at the time.

Mr. Murdoch’s family owns 29.5% of the voting shares. News Corporation on November 8 adopted a plan to protect against a hostile bid. Mr. Malone said on November 12 that his plan to acquire more voting shares was “entirely friendly” and that he supports Mr. Murdoch.

A News Corporation spokesman, Andrew Butcher, declined to comment on Mr. Malone. There is no “direct impact” on Mr. Malone from this transaction, Joyce said.

“What he’s trying to do is still open to speculation,” Mr. Joyce said.