SEOUL, South Korea — North Korea issued standing orders on Wednesday for the “miserable dog’s death” execution of South Korea’s imprisoned former president and her spy chief, and improbably demanded that its southern adversary extradite them.

The execution orders, which the North said could be carried out anytime, anywhere and by any means, amounted to an assassination decree against the imprisoned former president, Park Geun-hye, and Lee Byung-ho, who was director of the National Intelligence Service under Ms. Park.

Conveyed in a statement issued via North Korea’s official news agency, the execution orders came nearly two months after the isolated, nuclear-armed country accused the South Korean intelligence service of conspiring with the C.I.A. to assassinate the North Korean leader, Kim Jong-un, using biochemical poisons.

“We declare at home and abroad that we will impose death penalty on traitor Park Geun-hye and Mr. Lee,” said the statement from the North’s Ministry of State Security, Ministry of People’s Security and Central Public Prosecutors Office. The statement said the pair’s crime was “hideous state-sponsored terrorism.”