North Korea on Wednesday warned of capital punishment against a former South Korean president and former spy chief for their alleged plot to assassinate North Korean leader Kim Jong-un.

The angry statement came after a Japanese media report that former South Korean President Park Geun-hye had instructed former National Intelligence Service Director Lee Byung-ho to oust Kim by any means -- including assassination. 

The latest claim came amid lingering tensions on the Korean peninsula over North Korea's nuclear and missile programs.

"Former President Park Geun-hye and former spy chief Lee Byung-ho as well as NIS agents can never make any appeal even though they meet miserable dog's death any time, at any place and by whatever methods from this moment," the North Korea Ministry of State Security said in an English-language statement carried by the country's official Korean Central News Agency.

The statement demanded South Korea immediately hand over Park and Lee to North Korea, claiming they committed what it claims is hideous state-sponsored terrorism against the North's supreme leadership.

North Korea also warned it will impose summary punishment without advance notice on those who organized, took part in or pursued the plot in case the US and South Korea again try to stage a terrorist attack against North Korean leader Kim Jong-un.

"We do not hide that should the US and the South Korean authorities defy this warning and challenge our resolute measure, they will be made to pay a dear price in an irresistible physical way," said the statement, which was also issued by the Ministry of People's Security and the Central Public Prosecutors Office.

When contacted by Yonhap, the NIS dismissed "as groundless" North Korea's allegation of South Korea's assassination plot against North Korean leader Kim.

The spy agency also said the North's "open threat" against South Korean citizens won't be tolerated at all.

Former President Park is not available for comment as she is in jail after being impeached in March for her involvement in a massive corruption scandal that toppled the nation and resulted in a presidential election in May. (Yonhap)