North Korea has issued new threats against South Korea, vowing "sledge-hammer blows" of retaliation if the its southern neighbour did not apologise.
The United States says it will soon send a missile defence system to Guam to defend it from "a real and clear danger" from North Korea.
UN secretary general Ban Ki-moon has condemned North Korea's nuclear test, saying it is a "grave violation" of UN Security Council resolutions.
North Korean leader Kim Jong-un called for an end to confrontation between the two Koreas in a surprise New Year speech broadcast on state media.
North Korea's ruling party has removed a top military official close to the centre of power, suggesting Kim Jong-un may be purging the ruling elite.
North Korea in a policy-setting message for New Year called on its people to rally behind anointed successor Kim Jong-un by becoming "human shields".
South Korea said on Monday it was open to dialogue with Pyongyang if the North was ready to dismantle its nuclear facilities.
North Korea on Saturday called for an end to confrontation with the South, urging dialogue after one of the most violent years on the peninsula.
South Korean President Lee Myung-bak called for national solidarity on Monday against military aggression by the North.
Kim Tae-young, South Korea's defence minister, has resigned two days after an attack by North Korea and amid criticism on the South's response.