North Korea's leader has warned of an "all-out" war against the South while denouncing its ongoing joint military drill with the United States, state media said Sunday.

The US and South Korean militaries on Monday began a two-week exercise aimed at testing defences against the communist North, insisting it was defensive in nature but Pyongyang called it a drill for a preemptive nuclear attack.

More than 30,000 US troops, including most of those based in the South plus 3,000 from overseas, are taking part in the annual joint drill known as Ulchi Freedom Guardian.

North Korean leader Kim Jong-un called the drill a grave threat and said his army was ready to deal "deadly blows" if their territory was violated during the exercise.

"If the enemies fire even a single shell on our inviolable territory... the whole army should turn out as one and lead the battle to an all-out counter-offensive," said the leader, according to KCNA news agency.

The courageous officers... are now waiting for a final order for charge for a life-and-death battle against the enemies," Kim was quoted as saying in a speech to army officials Saturday. "There is a limit to our patience."

Kim, believed to be in his late 20s, took over the impoverished but nuclear-armed nation after his late father and longtime ruler Kim Jong-Il died last December.

On the eve of the ongoing drill, the young leader visited a frontliner artillery unit that carried out a deadly 2010 bombardment of a South Korean island near the disputed western sea border.

Kim praised its personnel as heroes and told them never to tolerate enemy aggression.

The two Koreas have remained technically at war since their 1950-53 conflict ended in an armistice, without a subsequent peace treaty.

Cross-border tensions have been high since the South accused the North of torpedoing one of its warships with the loss of 46 lives in March 2010.

The North angrily denied involvement but went on to shell the Yeonpyeong island in November of the same year, killing four South Koreans including two civilians.