The North also vowed to increase its nuclear strike force "in quality and in quantity", two days after its fifth test in a decade sparked international condemnation and moves for tougher UN sanctions.
In Japan, a visiting senior US envoy said Washington and Tokyo were seeking "the strongest possible" measures in response.
North Korea insists that its missile and nuclear tests are necessary to counter what it says is a US nuclear threat to its independence.
"Obama is trying hard to deny the DPRK's (North Korea's) strategic position as a legitimate nuclear weapons state but it is as foolish an act as trying to eclipse the sun with a palm," said the statement quoted by the official KCNA news agency.
Friday's test came only eight months after the previous one and was almost twice as powerful, at an estimated 10 kilotons.
Most worryingly for the international community, the North claimed it had been a miniaturised warhead that could be mounted on a missile.
Sung Kim, the US State Department's special representative for North Korea policy, said Washington and Tokyo would work closely in the Security Council and beyond "to come up with the strongest possible measure against North Korea's latest action".
He also suggested the US may launch its own unilateral sanctions in response to "the provocative and unacceptable behaviour by the North Koreans".
KCNA insisted today that North Koreans were delighted by Friday's detonation.
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