WASHINGTON — A few weeks in advance of the release of Bob Woodward’s new book on the Bush administration, speculation is surging that it will portray the latest phase of the war in Iraq as a success, credited to the recently departed commander of forces there, General David Petraeus.

Almost nothing has appeared in the press about the book, “A War Within: A Secret White House History,” and The New York Sun has been unable to reach anyone who has read the manuscript. But one source familiar with an early draft said Mr. Woodward had extensive access to General Petraeus and his deputies, known in the military as the “Jedi Council.” Mr. Woodward also interviewed the head of the Anbar Awakening, Sheik Ahmad al-Rishawi, who took over the Sunni Arab uprising against Al Qaeda in Iraq after his brother was assassinated last September.

Mr. Woodward’s new book is set to be published by Simon & Schuster on September 8. According to the source familiar with a draft, Mr. Woodward claims:

• Admiral James Fallon, the former head of Central Command, was pushed out of his post in part because of his clashes with General Petraeus, who was confirmed in June by the Senate to take over Central Command, a battle space that comprises Iraq and Afghanistan.

• Inside the Bush administration, General Petraeus effectively had the last word on policy inside Iraq. He was treated as an equal to Defense Secretary Gates and Secretary of State Rice in policy matters on Iraq.

• Much of the early reporting on the success of the military surge against Al Qaeda and Iranian-related special groups has been understated in recent press reports.

The new book will be the fourth volume in Mr. Woodward’s series on the Bush administration and its approach to the war on terrorism. His 2006 book, “State of Denial,” shattered much of the remaining support within the Washington elite for the president’s war policy. That book disclosed that the Pentagon had assessed in May 2006 that events in Iraq would become even more violent in 2007. In some ways the prediction was accurate, but by the middle of that year, the new counterinsurgency strategy implemented by General Petraeus had stemmed the casualties. This year, the American casualty statistics for July are lower than at any point since the 2003 invasion.

Representatives from Simon & Schuster did not offer a comment for this article. The book is likely to be excerpted next month in the Washington Post.