The book, "A Very Stable Genius" by Philip Rucker and Carol Leonnig, highlights episodes of volatile behavior by the president along with his ignorance of basic geography and history.
"It's not like you've got China on your border," the authors quoted Trump as telling Indian Prime Minister Narendra Modi during a meeting between the two leaders.
India and China share a border and the two countries went to war in 1962 over a disputed Himalayan section of the frontier.
Following Trump's border comment and seeming dismissal of the threat China poses to India, "Modi's eyes bulged out in surprise," according to the book, excerpts of which were published in the Post on Wednesday.
"Modi's expression gradually shifted, from shock and concern to resignation," it said.
After the meeting, "the Indians took a step back" in their diplomatic relations with the United States, a Trump aide told the authors.
The book also recounts a tour by Trump of a memorial for the USS Arizona, a US warship that was sunk by Japanese planes in the December 7, 1941 surprise attack on Pearl Harbour.
"Hey, John, what's this all about? What's this a tour of?" Trump is quoted as asking his then-chief of staff John Kelly.
"Trump had heard the phrase 'Pearl Harbor' and appeared to understand that he was visiting the scene of a historic battle, but he did not seem to know much else," the book said.
"He was at times dangerously uninformed," the book quotes a former senior White House adviser as saying.
The book said Trump lobbied then secretary of state Rex Tillerson in 2017 to help get rid of the Foreign Corrupt Practices Act which prevents US firms from bribing foreign officials for business deals.
"It's just so unfair that American companies aren't allowed to pay bribes to get business overseas," Trump is quoted as saying. "We're going to change that."
The book also recounts an exchange between Trump and Anthony Scaramucci, who served briefly as White House communications director and is now a fierce critic of the president.
Scaramucci said he once asked Trump, "Are you an act?"
"I'm a total act and I don't understand why people don't get it," Trump reportedly replied.
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