North Korean leader Kim Jong-un sees Donald Trump as a "new father figure" and is "fascinated" by him, according to a new book.

Author Doug Wead claims that Mr Trump admitted there was good "chemistry" between the two, reports Fox News.

"Kim is fascinated by Donald Trump. He sees him as a unique figure on the stage of world history. And he wants to make history with him," claimed Mr Wead in his book Inside Trump's White House: The Real Story of His Presidency.

In recent months, US has improved diplomatic relations with North Korea, but continues working towards an agreement on the rogue nation's nuclear programme.

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After a prolonged standoff that included fiery rhetoric and multilateral sanctions, President Trump took the historic leap of meeting the Supreme Leader.

US President Donald Trump meets with North Korean leader Kim Jong-un at the North Korean side of the border at the Demilitarised Zone. Photo / AP
US President Donald Trump meets with North Korean leader Kim Jong-un at the North Korean side of the border at the Demilitarised Zone. Photo / AP

However, the relationship didn't start off robust, with Kim regularly attacking Trump's mental stability, while Mr Trump made a mockery of Kim's physique.

Despite all the initial drama, the president told Mr Wead that he and Kim had good "chemistry" and they both wanted to steer clear of conflict.

"I firmly believe that the strong will, sincere efforts and unique approach of myself and your Excellency, Mr President, aimed at opening up a new future between the DPRK and the US will surely come to fruition," he said.

Trump's son-in-law Jared Kushner suggested Kim had problems with Trump because of issues surrounding his own father.

"Put it there." - U.S President Donald Trump with North Korea's leader Kim Jong-un. Photo / AP

"'It's a father thing,' Kushner observed. 'You can see from these letters that Kim wants to be friends with Trump, but his father told him never to give up the weapons. That's his only security. Trump is like a new father figure. So, it is not an easy transition.'"

In the book, Mr Wead portrays the Trump administration as much more diplomatic than President Obama.

"Barack Obama told me that my greatest problem, when I became president, was the possibility of war with North Korea. In fact, privately, he said, 'You will have a war with North Korea on your watch.'" Mr Trump said, according to Wead.

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Mr Trump responded by asking if Obama had tried talking with kim. "And Obama said, 'No, he's a dictator,'" Mr Trump reportedly said.

Donald Trump said that decision was "stupid."