North Korea on Sunday vowed tough action against the United States, accusing it of plotting to blow up statues of its founding leader in a bid to stir turmoil in the isolated communist state.

The warning comes just days after the North said it would "completely review" the nuclear issue, amid concerns that Pyongyang may be planning a third nuclear test following its failed rocket launch in April.

Pyongyang has recently increased hostility towards Seoul and Washington, accusing them of sending a spy to the country with a mission to blow up statues of Kim Il-Sung, adding that the plot amounted to a "war action".

"(North Korea) has various types of strike means... powerful enough to render the US modern war means ineffective," the country's National Defence Commission said in a statement carried by the state-run KCNA news agency.

It vowed to launch a "powerful physical counter-offensive" against the United States, but did not elaborate on what that meant.

The threat comes after the North arrested a man who was allegedly trying to blow up a monument to Kim Il-Sung.

Jon Yong-Chol was presented at a press conference in Pyongyang earlier this month, where he claimed he had been promised handsome rewards from Seoul intelligence agents if he succeeded in his mission.

The impoverished but nuclear-armed North has a pervasive personality cult surrounding its ruling family and has built numerous monuments for its late founding leader Kim Il-Sung who died in 1994 and his son Kim Jong-Il.

In April two giant statues of the two late rulers were unveiled in the capital Pyongyang, just hours after the North's failed rocket launch seen by the US and its allies as an attempted ballistic missile test.