South Korea says it will not back down to North Korea.
In address to mark the South's Memorial Day, President Lee Myung-bak said on Saturday: "There should be no doubt that there will be no compromise against things that threaten our people and security."
He said there was "no reason to fear" as South Korea has "a strong defence."
North Korea conducted a nuclear test on 29 May - its second since October 2006. In addition, a number of short-range missiles were fired last week.
KCNA, an official media agency in Pyongyang, reiterated a warning of "strong action" on Saturday, blaming the South for increasing military tension.
It said South Korea "should not make any reckless move" as "anyone making provocation will be met with strong action and unimaginable punishment".
The two Koreas are due to hold talks next week over a joint industrial park that was once a symbol of reconciliation between the two states,.
North Korea in May declared all contracts in the park invalid. About 100 South Korean small and medium sized companies use cheap North Korean labour to make goods at the Kaesong industrial enclave.