“This is another intolerable and grave provocation to us, and a reckless challenge to the public opinions at home and abroad,” the North’s Committee for the Peaceful Reunification of the Fatherland said in a statement.
“The South Korean puppets will never avoid a stern punishment by our military and people, and also strong protests from the southern people if they continue the smear campaign against the DPRK [North Korea].”
The committee, which handles North Korea’s relations with the South, did not elaborate on the form of retaliation it would take.
South Korea has said it wants the 15-member Security Council to “respond in a manner appropriate to the gravity of North Korea’s military provocation in order to deter recurrence of any further provocation by North Korea”.
The request came as South Korea’s president toned down public criticism of the North, pledging to seek a lasting peace on the Korean peninsula.
Lee Myung-bak said in a nationally televised speech on Sunday that his country has “an unachieved dream” of peace and prosperity with the North.
Lee also said his government would strive to defend the country and revive the economy, but he stopped short of directly criticising North Korea in the speech.
South Korean leaders traditionally use the Memorial Day speech to emphasise efforts toward peace.
However, the United States and its Asian allies have said North Korea must be held accountable for the sinking of the Cheonan.
Defence ministers from the US, Japan and South Korea met in Singapore at the weekend to weigh punitive steps against North Korea.
Robert Gates, the US defence secretary, told his counterparts on Saturday that “it’s important we have a unified front to deter further provocations”, his press secretary told reporters.
But in a BBC interview broadcast on Sunday Gates said there were few, if any, effective options against North Korea, short of military action.