Tensions between the rogue state and its enemies, South Korea and the USA, have been heightened in recent months, since it was revealed that North Korea had developed its weapons to the point where the U.S. mainland was within striking distance.
Kim Jong-un has ordered North Korea's military scientists to boost production of more effective missiles that can be launched faster and hidden more easily, making the country less vulnerable to a pre-emptive strike.
North Korea has conducted two nuclear tests and dozens of missile tests since the beginning of past year, including ICBM tests.
"But Kim Jong-un, I respect the fact that I believe he is starting to respect us".
A series of threats followed from both sides, and while the rhetoric has since eased, the US and South Korea this week kicked off their annual Ulchi Freedom Guardian military drills, which the North always condemns as dress rehearsals for invasion.
According to Yonhap, which in turn cites KCNA, Kim "has ordered the production of more solid-fuel rocket engines and warhead tips for intercontinental ballistic missiles (ICBMs) during his inspection of a chemicals institute".
"Some people said it was too strong. It's not strong enough", he told a gathering of thousands of supporters at a campaign style rally in Phoenix, Arizona. "I respect that fact very much", he said.
'And maybe - probably not, but maybe - something positive can come about, ' he said.
Kim Jong-un has ordered production of more missiles and rocket engines
U.S. Secretary of State Rex Tillerson also noted on Tuesday that North Korea has demonstrated "some level of restraint" since the UN Security Council adopted new sanctions against it.
North Korea claims it can miniaturize a nuclear device to fit onto a missile.
"He instructed the institute to produce more solid-fuel rocket engines and rocket warhead tips", it added.
Such casings are harder to manufacture than metal ones but are much lighter, enabling longer ranges and heavier payloads.
"I don't think there's any accident about this, the shot clearly shows Pukguksong-3, this was the North Koreans showing us what we could possibly see soon", he said.
Kim Jong-un has threatened to fire missiles at the island of Guam, where the USA has its foothold in the Pacific Ocean - a key strategic location.
Trump has urged Beijing, North Korea's only major ally, to bring greater pressure to bear in reining in its neighbour's nuclear efforts, suggesting that the United States may offer concessions on trade in return.
"The U.S. will be wholly held accountable for the catastrophic consequences to be entailed by such reckless aggressive war maneuvers, as it chose a military confrontation [with North Korea]", a North Korean military spokesman said.