US President Donald Trump says North Korea’s Kim Jong-un wants to meet once again to “start negotiations” after joint US-South Korea military exercises end.

He also says Mr Kim apologised for the flurry of recent short-range missile tests that has rattled US allies in the region.

Mr Trump has been tweeting more details from the “beautiful” three-page letter he told reporters on Friday he’d received from Mr Kim.

Mr Trump, who is on holiday at his golf club in New Jersey, said Mr Kim spent much of his letter complaining about “the ridiculous and expensive exercises”, which North Korea sees as a threat.

He said Mr Kim offered him “a small apology” for the recent tests and assured him “this testing would stop when the exercises end”.

In a letter to me sent by Kim Jong Un, he stated, very nicely, that he would like to meet and start negotiations as soon as the joint U.S./South Korea joint exercise are over. It was a long letter, much of it complaining about the ridiculous and expensive exercises. It was…..

— Donald J. Trump (@realDonaldTrump) August 10, 2019

North Korea on Saturday fired what appeared to be two short-range ballistic missiles into the sea, the fifth round of launches in less than three weeks.

North Korea’s official news agency KCNA reported on Sunday the missile launch was of a newly developed weapon which “has advantageous tactical character different to the existing weapon systems”.

Mr Kim “guided the test-fire” of the weapon “developed to suit the terrain condition” of the country, KCNA reported.

Meanwhile, Pyongyang and Washington are currently trying to relaunch stalled talks on North Korea’s nuclear weapons programmes and economic sanctions.

“I look forward to seeing Kim Jong-un in the not too distant future!” Mr Trump wrote on Saturday.

The two leaders have met three times – in Singapore, Hanoi and at the Korean Demilitarised Zone – but critics say Mr Trump has received few concessions in the stand-off over North Korea’s nuclear weapons program.

At their second summit in Vietnam in February, Mr Trump rejected Mr Kim’s demand for widespread sanctions relief in exchange for dismantling the North’s main nuclear complex, a partial disarmament step.

The US and South Korea have scaled down their major military exercises since Mr Trump and Mr Kim’s first summit in June 2018.

But the North insists even the downsized drills violate agreements between Mr Kim and Mr Trump and compel it to “develop, test and deploy the powerful physical means essential for national defence”.

When they last met in June of this year, Mr Trump and Mr Kim agreed to resume working-level nuclear talks that have been stalled since February, but there have been no known meetings between the two sides since then.

-AAP