Bancroft family members, who control 64 percent of the information company's voting shares, are weighing the offer, Dow Jones said. The family is set to meet Monday, according to The Wall Street Journal, Dow Jones' flagship asset.
According to the newspaper, board members Leslie Hill and Dieter von Holtzbrinck abstained from the vote; Christopher Bancroft -- who has been actively seeking alternatives to the News Corp. bid -- left the meeting early. Two other Bancroft directors, including family trustee Michael Elefante, voted in favor of the deal.
News Corp. said in a statement it was grateful to the Dow Jones board for its "strong vote of support."
News Corp. proposed in April to buy all outstanding shares of Dow Jones' common and Class B stock for $60 per share.
The 65 percent premium was applauded by many investors, although a number of Bancrofts opposed the bid because they maintain that Murdoch would use Dow Jones' celebrated news operations, particularly the Journal, to buttress his business interests.
Besides the Journal, Dow Jones publishes the Barron's investor newspaper, the MarketWatch.com financial news Web site, and Dow Jones Newswires, rival to Reuters Group and Bloomberg in providing financial news.
News Corp. owns the Fox broadcast network, Fox News Channel, newspapers in the United Kingdom, Murdoch's native Australia and the New York Post, the Twentieth Century Fox movie and TV studio and MySpace, the online social networking site.
The Bancrofts own 25 percent of Dow Jones but control 64 percent of the company's shareholder vote through a special class of shares that have ten votes each versus one vote for every publicly held share.
News Corp. and Dow Jones declined to indicate how board members voted.
The possibility reportedly remains that sufficient numbers of the Bancroft family members and other Class B shareholders could block a deal with Murdoch.
Analysts have said the deal's failure could drag down Dow Jones's share price.
Murdoch resisted pressure from Dow Jones to raise his initial $60 a share offer, which represented a huge premium of about 65% over the mid-$30s level that Dow Jones stock was trading at before the proposal became public in early May.
Murdoch has long wanted to own the Journal, along with its clout on Wall Street and a history of outstanding journalism. Murdoch has said he would invest in the Journal's online and overseas operations, and help build a business-themed cable news channel that would rival General Electric's highly profitable CNBC network.
A union representing Journal reporters and other Dow Jones employees has objected to Murdoch's bid, saying he would downgrade news coverage and interfere with newsroom independence for his own business interests.
The Bancrofts originally rebuffed Murdoch's approach but then agreed to meet with him in early June. The two sides agreed to form a committee that would approve the hiring or firing of top editors at the Journal to ensure independence.
Dow Jones directors have been searching for rivals to Murdoch's $5 billion bid, but it seemed unlikely that anyone can top it.
A committee of Dow Jones directors, including a representative of the Bancroft family, met last week with supermarket billionaire Ron Burkle and Web entrepreneur Brad Greenspan, but no counteroffer has emerged. Earlier, General Electric and Pearson abandoned exploratory talks to combine GE's CNBC channel with Dow Jones and Pearson's Financial Times newspaper.