The United States hopes to one day normalise relations with North Korea, President Trump said, adding that he would invite North Korean leader Kim Jong-un to the United States if next week's historic summit goes well.

Trump signalled that a grand bargain to reverse decades of enmity is not on the table for his unprecedented meeting on Tuesday in Singapore with Kim, but sounded upbeat as he described the North Korean leader as sincere about remaking the future for his impoverished country.