US President Donald Trump wanted to have Syrian President Bashar al-Assad assassinated last year but his defence secretary ignored the request, according to a new book that depicts top Trump aides sometimes disregarding presidential orders to limit what they saw as damaging and dangerous behaviour.

Excerpts from the book, Fear: Trump in the White House, written by famed Watergate reporter Bob Woodward, were published by the Washington Post on Tuesday. The book, which is scheduled for release on September 11, is the latest to detail tensions within the White House under Trump's 20-month-old presidency.

'It's just another bad book,' Trump told the Daily Caller.

The Republican president said in a Twitter post that quotes in the book attributed to Defense Secretary James Mattis, White House Chief of Staff John Kelly and others 'were made up frauds, a con on the public'.

The book portrays Trump as prone to profane outbursts and impulsive decision-making, painting a picture of chaos that Woodward says amounts to an 'administrative coup d'etat' and a 'nervous breakdown' of the executive branch.

According to the book, Trump told Mattis that he wanted to have Assad assassinated after the Syrian president launched a chemical attack on civilians in April 2017.

Mattis told Trump he would 'get right on it,' but instead developed a plan for a limited air strike that did not threaten Assad personally.

Mattis told associates after a separate incident that Trump acted like 'a fifth- or sixth-grader', according to the book.

In a statement on Tuesday, Mattis dismissed the book as 'a uniquely Washington brand of literature' and said the contemptuous words about Trump attributed to him 'were never uttered by me or in my presence'.

White House spokeswoman Sarah Sanders said the book was 'nothing more than fabricated stories, many by former disgruntled employees, told to make the president look bad'.

Nikki Haley, the US ambassador to the United Nations, cast doubt on the account about Assad.

'I have the pleasure of being privy to those conversations...and I have not once heard the president talk about assassinating Assad,' Haley told reporters on Tuesday.

Woodward gained national fame for his reporting on the Watergate scandal in the 1970s, and has since written a number of books that provide behind-the-scenes glimpses of presidential administrations and other Washington institutions. For this book, Woodward spoke to top aides and other insiders with the understanding that he would not reveal how he got his information, the Post reported.

Among his other revelations: former top economic adviser Gary Cohn stole a letter off Trump's desk that the president planned to sign that would withdraw the United States from a trade agreement with South Korea.

Cohn, who tried to rein in Trump's protectionist impulses, also planned to remove a similar memo that would have withdrawn the United States from the North American Free Trade Agreement with Mexico and Canada, Woodward wrote.

'I'll just take the paper off his desk,' Cohn told another White House aide, according to the book.

Trump said that did not take place. 'It's just made up,' he told the Daily Caller.

The United States remains part of both trade agreements as it negotiates new terms.

'Worst job' ever

Other aides insulted Trump behind his back. Kelly called Trump an 'idiot' and said, 'We're in Crazytown. ... This is the worst job I've ever had.'

Trump treated top aides with scorn, the book says, telling Commerce Secretary Wilbur Ross that he was past his prime and calling Attorney General Jeff Sessions 'mentally retarded'.

In a tweet late on Tuesday, Trump said Woodward wrote that he also called Sessions 'a dumb southerner'.

'I said NEITHER, never used those terms on anyone, including Jeff, and being a southerner is a GREAT thing. He made this up to divide!' Trump said in the tweet.

Kelly, in remarks released by the White House, said he never called the president an idiot and called the story 'total BS'.

Trump has grown paranoid and anxious over an ongoing federal inquiry into whether his campaign colluded with Russia in Moscow's alleged interference in the 2016 presidential election, prompting aides to compare Trump to former President Richard Nixon during the Watergate scandal, Woodward reported.

Trump's former lawyer John Dowd conducted a mock interview with Trump to convince him that he would commit perjury if he agreed to talk to Special Counsel Robert Mueller, who is leading the Russia investigation, the book says.

Trump did not speak with Woodward until the manuscript was complete, the newspaper reported. 'So I have another bad book coming out. Big deal,' Trump told Woodward, according to a transcript of a telephone call released by the Post.