Lowongan Kerja - Earlier reports said a security aide would succeed Mr Kim, who resigned after North Korea surprised Seoul by shelling a Southern island. Tuesday's barrage killed four people and sent regional tensions soaring.
The office of South Korean President Lee Myung-bak said several candidates were undergoing rigorous checks, denying local reports of a decision. - Job Vacancy
Job Indonesia - On Friday, Pyongyang said joint US-South Korean naval exercises planned for next week would take the region "to the brink of war".
The North's state news agency, KCNA, said the exercises were "reckless" and the "trigger-happy" allies were deliberately targeting the North.
The North Korean artillery shelling - which killed two South Korean civilians and two marines - was one of the worst incidents between the two Koreas since the end of the Korean war in 1953, which concluded without a peace treaty.
'Reckless provocation' President Lee Myung-Bak accepted Mr Kim's resignation "to improve the atmosphere in the military and to handle the series of incidents," a presidential official said.
Earlier on Friday local news agencies reported that Lee Hee-Won, 61, had been named as new defence minister. Mr Lee is a former four-star general who became deputy chief of the US-South Korea Joint Forces Command in 2005.
He retired from the military in 2006 and was made a presidential security advisor in May following the sinking of the Cheonan, a South Korean warship.
In response to Tuesday's incident South Korea has increased troop numbers on the island, Yeonpyeong, and has said it is changing its rules of engagement to allow it to respond more forcefully to similar incidents. The old rules have been criticised as too passive.
Whoever is appointed will now have the opportunity to overhaul the country's security apparatus, says the BBC's Chris Hogg in the South Korean capital, Seoul.
The cabinet had decided that under the old rules of engagement there was too much emphasis on preventing a military incident escalating into something worse, our correspondent adds.
In future, the South would implement different levels of response depending on whether the North attacked military or civilian targets, a presidential spokesman said.
The US aircraft carrier group led by the USS George Washington is meanwhile on its way to participate in exercises with the South Korean navy - a move arranged before the incident with the North.
North Korea has warned it will "wage second and even third rounds of attacks without any hesitation if warmongers in South Korea make reckless military provocations again".