US President Donald Trump has claimed that following his summit with Kim Jong-un that he has "largely solved" the North Korean nuclear problem.

Speaking to reporters outside the White House, Mr Trump said former president Barack Obama told him before he took office that the "most dangerous problem" for the United States was North Korea's nuclear weapons programme.

"I have solved that problem," Mr Trump said. "Now we're getting it memorialised and all but that problem is largely solved."

"We signed a very good document," he said. "But more importantly than the document I have a good relationship with (North Korean leader) Kim Jong-un.

"That's a very important thing. I can now call him," he said. "I gave him a very direct number. He can now call me if he has any difficulty. We have communication.

"People are shocked," the president continued. "They thought Trump was going to get in, he's going to start throwing bombs all over the place. It's actually the opposite."

"I'm going to be actually calling North Korea," Mr Trump told Fox News in an interview earlier today when asked what he planned to do on Father's Day.