'If not for me, we would now be at war with North Korea!': Trump

US President Donald Trump has said talks with North Korea are going well, just days after Trump declared the country an "unusual and extraordinary threat" to American national security, despite a historic recent summit with North Korean leader Kim Jong-un.

"Many good conversations with North Korea-it is going well!"Trump wrote in a post on Twitter on Tuesday.

“If not for me,” he added, “we would now be at War with North Korea!”

Following their meeting on June 12 in Singapore, the first between a sitting US president and a North Korean leader, Trump and Kim signed a joined document, committing to establishing new relations and achieving peace on the Korean Peninsula.

Before signing the document, Kim said the two leaders had “decided to leave the past behind” and that “the world will see a major change.”

Trump said he had formed a “very special bond” with Kim and that Washington’s relationship with Pyongyang would be very different.

But last week, Trump declared North Korea an "unusual and extraordinary threat" to the US as he acted to maintain harsh economic sanctions against Pyongyang.

The national emergency Trump signed will keep in place sanctions first imposed a decade ago by President George W. Bush.

It also allows Washington to bar North Korean leaders from selling or using any assets they may hold in the United States. It is separate from US sanctions related to the North’s human rights issues and international penalties imposed over its nuclear and ballistic missile programs.

The document says the US and North Korea “commit to establish [sic] new... relations in accordance with the desire of the peoples of the two countries for peace and prosperity."

Trump has sounded a triumphant tone since the Singapore summit, but his critics have pointed to the vague wording of the non-binding document, which Trump called a "deal”.

US nuclear stand-off with North Korea 'largely solved'

Trump has said Washington's nuclear stand-off with North Korea "largely solved".

Trump told reporters three days after the summit with Kim that he is now in direct contact with Kim and that their "good relationship" had ended the risk of conflict.

"I have solved that problem," Trump told reporters. "Now we're getting it memorialized and all, but that problem is largely solved."

"We signed a very good document," he added. "But more importantly than the document, I have a good relationship with Kim Jong-un," he added. 

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

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