North Korean leader Kim Jong Un's powerful sister has demanded a detailed "explanation" from Seoul over a drone it accused South Korea of flying over its territory, state media reported Sunday.

The North alleged on Saturday that a craft crossed from the South Korean border county of Ganghwa into the North Korean city of Kaesong in early January, and released photos of wreckage from the drone it claimed to have shot down.

Seoul rejected the claim, with its defence ministry saying the drone was not a model operated by its military.

"Fortunately, the ROK's military expressed an official stand that it was not done by itself and that it has no intention to provoke or irritate us," Kim Yo Jong said, using South Korea's official name in a statement carried by the state-run Korean Central News Agency (KCNA).

"But a detail [sic] explanation should be made about the actual case of a drone that crossed the southern border of our Republic," she said, according to KCNA.

In response to the North's accusation, Seoul's military said its own investigation had revealed it does not "possess the unmanned aerial vehicle in question, nor did it operate any unmanned aerial vehicles at the time and date specified by North Korea".

President Lee Jae Myung on Saturday ordered a "swift and rigorous investigation" by a joint military-police investigative team.

On the possibility that civilians operated the drone, Lee said: "If true, it is a serious crime that threatens peace on the Korean Peninsula and national security."

But Kim said she did not care whether it was a military or civilian drone, saying "that is not the one (detail) we want to know".

"Clear is just the fact that the drone from the ROK violated the airspace of our country," she added, according to KCNA.

Kim ended her statement calling South Korea "a group of hooligans and scrap".

Analysts said Kim Yo Jong's statement suggested Pyongyang wanted to treat the issue as a diplomatic matter.

"Pyongyang has indicated it has no intention of turning this into a military issue through Kim's statement," said Hong Min, an analyst at the Korea Institute for National Unification.

But her demand for an explanation "signals a shift toward a diplomatic offensive by holding the authorities accountable" for the incursion, he told AFP.

The new drone allegation comes as former president Yoon Suk Yeol is standing trial on charges that he illegally ordered drone operations, hoping to provoke a response from Pyongyang and use it as a pretext for his short-lived bid to impose martial law.

Yoon was impeached and removed from office in April last year over his martial law attempt.