The North issued a similar warning in September before it conducted a nuclear test earlier this month, prompting the UN Security Council to impose financial and arms sanctions on North Korea.
South Korea's participation in sanctions would be seen as a serious provocation leading to a "crisis of war" on the Korean peninsula, a North Korean official said in a statement carried by the official KCNA news agency.
South Korea's involvement in sanctions against the North is important because the country is one of the main aid providers to the impoverished communist state, along with China.
How to enforce the sanctions has also been an issue between the US and China, the North's last-remaining major ally. Beijing voted for the UN resolution and says it would meet its obligations, but is concerned that excessive measures could worsen the situation.
Still, the US envoy to six-party talks on halting North Korea's nuclear programme said Pyongyang's nuclear test brought Washington and Beijing closer.
In its first official confirmation of the North's nuclear test, South Korea's science and technology ministry said on Wednesday that xenon - an inert gas released when there is a nuclear explosion - has been found in air samples collected in South Korea.
The finding corroborates a US government confirmation last week that cited radioactive debris detected in air samples.
In the meantime, Lee Jong-seok, South Korea's unification minister, has offered to resign, in what may be a major reshuffle of the national security team triggered by the departure of Ban Ki-moon, the foreign minister.
The shake-up comes as South Korea considers its next steps after North Korea conducted its first nuclear test on October 9, defying international warnings and forcing UN sanctions.
Unification minister Lee, a North Korea expert, has been criticised for not being tough enough against Pyongyang.
But he has also been praised for managing bilateral ties with the North during a difficult time as Pyongyang took successive steps to escalate tensions, first by test-launching missiles in July and then with its nuclear device.