The statement by Kim Yo Jong came a day after the nuclear-armed North fired what appeared to be two short-range ballistic missiles off its east coast on Saturday, the latest such action it has taken this year.

"In the letter, he... explained his plan to propel the relations between the two countries of the DPRK and the US and expressed his intent to render cooperation in the anti-epidemic work," an apparent reference to the coronavirus pandemic, Jong said in the statement reported by the North's Korean Central News Agency (KCNA).

While the letter reflects "excellent" ties between the two leaders, she warned that broader relations between their two nations are different.

"We try to hope for the day when the relations between the two countries would be as good as the ones between the two top leaders, but it has to be left to time and be watched whether it can actually happen," Jong said.

There was no immediate comment from the White House on the letter.

Analysts say the North has been continuing to refine its weapons capabilities more than a year after a summit between Kim and Trump broke down in Hanoi. The deadlock is over sanctions relief and what North Korea would be willing to give up in return.

Pyongyang is under multiple sets of United Nations, US and other sanctions over its weapons programmes.

Jong praised Trump's "efforts to keep the good relations he had with our Chairman by sending a personal letter again at a time as now when big difficulties and challenges lie in the way of developing the bilateral relations."

But she said "nobody knows how much the personal relations would change and lead the prospective relations between the two countries, and it is not something good to make hasty conclusion or be optimistic about it."

Trump, whose closeness to Kim and other global strongmen has raised concerns at home, is seeking re-election in November's US election.

Jong said bilateral dialogue "would be thinkable only when the equilibrium is kept dynamically and morally and justice ensured between the two countries, not merely by the personal letter between the two leaders."

Pyongyang set Washington a unilateral end-2019 deadline to offer fresh concessions, and in late December Kim declared the North no longer considered itself bound by its moratoriums on nuclear and intercontinental ballistic missile tests.

He also threatened a demonstration of a "new strategic weapon" soon.

KCNA said that Kim on Friday oversaw an "artillery fire competition" among combined units of the army, using language similar to what it used after other exercises this year but which South Korea and Japan said appeared to be ballistic missiles.

Seoul's unification ministry earlier this month said the drills are aimed at strengthening "internal solidarity" and "attracting the attention of the US and South Korea and pressuring their change in attitude."

Shortly before the latest launch, KCNA reported that the rubber-stamp parliament, the Supreme People's Assembly, would convene on April 10.

The event would involve gathering nearly 700 officials in one place, analysts said. Such events have been banned in many parts of the world to curb the spread of new coronavirus.

Leif-Eric Easley, a professor at Ewha University in Seoul, told AFP earlier that Pyongyang is likely struggling with the pandemic, even though the regime has not reported any cases.

The UN Security Council has said it would make humanitarian exemptions to sanctions on North Korea to help it fight the coronavirus.