North Korea is threatening to introduce a new nuclear deterrent because of US hostility, amid tensions over a sunken South Korean warship.
It also accused the US of taking weapons into Panmunjom, the truce village in the demilitarised zone.
The statements came hours after US President Barack Obama urged his Chinese counterpart to take a stronger stance on the warship issue.
Investigators say North Korea sank the warship with a torpedo on 26 March.
Forty-six sailors died when the South Korean ship, the Cheonan, split in two and went down near the disputed inter-Korean maritime border.
South Korea is seeking a UN Security Council response over the incident, for which North Korea denies all responsibility.
The North Korean statement, carried by official news agency KCNA, did not give any details of how the communist country could bolster its nuclear capability.
"The recent disturbing development on the Korean peninsula underscores the need for (North Korea) to bolster its nuclear deterrent in a newly developed way to cope with the US persistent hostile policy toward (the North) and military threat toward it," it quoted the foreign ministry as saying.
North Korea has carried out two nuclear tests. It is thought to have both plutonium and uranium-based weapons programmes.
The BBC's John Sudworth, in Seoul, says the comments could also be meant as a hint that it is trying to build a hydrogen bomb, a massively more powerful weapon than the type it is already known to possess.
North Korea announced in May that it had successfully conducted a nuclear fusion reaction, the type used in a hydrogen bomb.
But that kind of breakthrough would require a major technological leap and many experts doubt whether North Korea has the facilities or the resources, our correspondent says.
In a second statement on Monday, North Korea accused the US of bringing weapons into Panmunjom, the truce village that lies in the demilitarised zone, on 26 June.
"Strong military counter-measures" would be taken if the weapons were not removed, the statement said.
US troops said that they were checking the report.
The two North Korean statements came as Mr Obama held what he called blunt talks with Chinese President Hu Jintao on the warship issue.
China's stance is key to any unified Security Council response, because it holds a veto.
Beijing has in the past opposed strong measures against Pyongyang because it fears the collapse of its impoverished neighbour.
Mr Obama said that while he understood China's position, there was "a difference between restraint and wilful blindness to consistent problems".