News Corp.'s board, under scrutiny for its supervision amid a reporting-tactics scandal at the U.K. newspaper division, is expected to sit tight for at least the next couple of weeks, comfortable that the steps the company has taken so far are appropriate for addressing the crisis, barring other significant developments, according to people familiar with the matter.

Critics, however, contend the board lacks the level of independence it needs to ensure the mess is cleaned up properly.

A week ago, News Corp. formalized a management and standards committee tasked with cooperating on investigations into voicemail interceptions and alleged improper police payments at its U.K. newspaper unit, "conducting its own enquiries" and proposing new standards. The committee ultimately reports to independent director Viet Dinh, who was an assistant attorney general under President George W. Bush.

However, the structure of the management committee, which reports through News Corp. Executive Vice President Joel Klein, raised questions about the board's ability to properly police the company. It also bolstered longstanding criticism about the lack of truly independent oversight at News Corp. overall.

Corporate-governance experts say any investigation into the company's conduct can't pass muster if it is overseen by a senior executive who reports to the chief executive and controlling shareholder, Rupert Murdoch.

"The probe cannot be conducted effectively while Mr. Murdoch is in charge," said Nell Minow, a corporate-governance specialist.

A spokeswoman for News Corp. said Mr. Klein, who is also a director, is reporting to the independent directors, not to Mr. Murdoch, on this investigation.

Ms. Minow is former editor of the Corporate Library, a governance research firm that recently merged with GovernanceMetrics International and has given News Corp. an "F" for its governance and board effectiveness every year since 2003. "I don't think there is such a thing as an independent director on that board.''

The board's independent directors are looking ahead to a previously scheduled meeting in Los Angeles before News Corp. reports quarterly earnings Aug. 10, according to the people familiar with the situation. Nine of News Corp.'s 16 directors are considered independent.

Though the independent directors have been holding regular Friday calls in recent weeks, next month's meeting will be the first time the group convenes in person since the phone-hacking scandal flared earlier this month, precipitating the closure of News Corp.'s News of the World tabloid and putting key executives on the firing line.

Board members have been discussing Elisabeth Murdoch joining the News Corp. board following News Corp.'s acquisition of the TV production company she runs, Shine Group, according to people familiar with the matter. One of those people said the plan is still for her to join the board.