Mr Trump's chief of staff and defence secretary, in responses posted by the president on Twitter, described the book as "pathetic" and "fiction".
In the book, senior aides are quoted as saying they hid sensitive documents to prevent Mr Trump signing them.
They are quoted as calling him an "idiot" and a "liar".
The book - Fear: Trump in the White House, scheduled for release on 11 September - reveals a chaotic administration having a "nervous breakdown of executive power".
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Woodward is a widely respected and veteran journalist who helped expose President Richard Nixon's role in the Watergate scandal in the 1970s.
How has the president responded?
He sent out a series of tweets carrying his own views, along with statements from Defence Secretary Jim Mattis, chief of staff John Kelly and White House spokeswoman Sarah Huckabee Sanders.
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Mr Trump says quotes attributed to Mr Mattis and Mr Kelly were "made up frauds, a con on the public. Likewise other stories and quotes".
He says the book is "already discredited" with "so many lies and phony sources", rejecting an allegation that he had used the terms "mentally retarded" and "dumb Southerner" to describe Attorney General Jeff Sessions.
The statement from Mr Mattis describes the book as "a product of someone's rich imagination" and adds: "The contemptuous words about the president attributed to me in Woodward's book were never uttered by me or in my presence."
The statement from Mr Kelly says: "The idea I ever called the president an idiot is not true... He always knows where I stand and he and I both know this story is total BS... This is a pathetic attempt to smear people close to President Trump."
Ms Sanders said the book was "nothing more than fabricated stories, many by former disgruntled employees, told to make the president look bad".
In an interview with the Daily Caller, Mr Trump said that "it's just another bad book", adding that Woodward "has a lot of credibility problems".
The president resumed his attack on the book in a tweet on Wednesday morning: