"This book is nothing more than fabricated stories, many by former disgruntled employees, told to make the President look bad," Sanders said.
The statement said Democrats and their allies in the press know the policies of US President Donald Trump are working, and no one would be able to beat him in the 2020 election.
Kelly also denied a quote attributed to him in the book in which he allegedly called Trump an "idiot."
The Washington Post reported earlier on Tuesday that Woodward's book, "Fear," is based on hundreds of interviews with first-hand witnesses and members of the administration, as well as meeting notes, personal diaries and government documents.
Woodward reportedly sought an interview with Trump on numerous occasions but did not get one until after the book was complete. According to an audio recording of the conversation, Trump called Woodward in August, after the book was completed, to say that he wanted to participate.