The demand comes a week after the North sensationally alleged it uncovered a US-South Korean plot
to kill Kim with biochemical, radioactive or poisonous substances during a major event, such as a military parade.
The prosecutors on Friday said outgoing South Korean National Intelligence Service (NIS) chief Lee Byung-ho and unnamed "masterminds in (the) CIA" are among those they intend to prosecute, North Korean state news agency KCNA reported.
Lee leads the NIS, though new South Korean President Moon Jae-in has nominated a replacement.
The prosecutors called for the arrests and extraditions of those they say led or were involved with "the hideous state-sponsored crime."
"The CIA can never dodge its responsibility for having played a mastermind role in the crime," the North's Central Public Prosecutor's Office said, according to KCNA.
Last week's KCNA report claimed that members of the CIA and NIS worked with a North Korean citizen in a plot to "commit bomb terrorism targeting the supreme leadership," and that the plot was "recently uncovered and smashed."
North Korea has a history of making unfounded claims, and CNN did not independently corroborate last week's report. US and South Korean intelligence officials dismissed the accusations
The alleged plot
KCNA last week described the alleged plot in great detail, saying it was hatched in 2014 when the South Korean and US intelligence agencies recruited a North Korean working in the timber industry in eastern Russia. Further contacts were made over subsequent years, and the assassination attempt was to have taken place at a military parade, KCNA said.
The KCNA report did not say when the alleged plot was stopped.
The accusations come amid high tensions between the US and North Korea, which in recent months ramped up missile
tests in defiance of UN Security Council resolutions.
As KCNA announced the allegations last week, it also said North Korea was embarking on a campaign to root out suspected foreign agents. In the last three weeks, North Korea announced it arrested two US citizens
working at a Pyongyang university on suspicion of "hostile acts" against the state.
History of unfounded claims
North Korea has a history of bombastic propaganda featuring unfounded claims.
Last month, the state-run newspaper Rodong Sinmun claimed
US-Australian military exercises in northern Australia were preparation for nuclear war against North Korea and threatened Darwin with a potential retaliatory strike.
Last year, lawmakers said Seoul "has a general idea and plan to use precision missile capabilities to target the enemy's facilities in major areas as well as eliminating the enemy's leadership."
The country's Joint Chiefs of Staff has prepared a system called the Korea Massive Punishment and Retaliation (KMPR) that would involve surgical missile attacks, exclusive special warfare units and an ability to strike North Korea's leadership if South Korea feels threatened by nuclear attack.