"Any attempt to deny the position of the DPRK as a nuclear weapons state... will be thoroughly rejected," Kim Yo Jong said in a statement carried by state media, referring to the North by the acronym for its official name.

Kim said the "personal relationship" between her brother and Trump was "not bad", but warned that should not be used to "serve the purpose of denuclearisation" in any future talks.

Trump and the North Korean leader met three times during the US president's first term in a bid to reach an agreement on the denuclearisation of the North.

But since their second summit in Hanoi in 2019 fell apart over failure to agree on what the North would get in return, Pyongyang has accelerated its nuclear programme.

"Shortly ago, a person in authority of the White House said... that he (Trump) is still open to dialogue with the DPRK leader for achieving the complete denuclearization of the DPRK," Kim Yo Jong said Tuesday, according to the North's official Korean Central News Agency.

She appeared to be referring to an unnamed White House official who was quoted by Yonhap news agency at the weekend as saying Trump "remains open to engaging with Leader Kim to achieve a fully de-nuclearized North Korea".

"I do not want to deny the fact that the personal relationship between the head of our state and the present US president is not bad", she said, but warned Washington against trying to use that to achieve denuclearisation.

If it is used for that purpose, "it can be interpreted as nothing but a mockery of the other party," she said, urging the United States to recognise the North as a "nuclear weapons state".

Trump has talked up his "great relationship" with the North Korean leader, and hinted that he might seek to rekindle talks with the third-generation ruler in Pyongyang.