North Korea says it has entered a "state of war" with South Korea.

"From this time on, the North-South relations will be entering the state of war and all issues raised between the North and the South will be handled accordingly," a statement carried by the North's official KCNA news agency said.

The announcement is the latest in a continuing escalation of angry rhetoric directed at South Korea and the United States.

Responding to the North Korean move, Russia urged restraint.

"We hope that all parties will exercise maximum responsibility and restraint and no-one will cross the point of no return," senior Russian Foreign Ministry official Grigory Logvinov told Interfax news agency.

A spokeswoman for the US National Security Council, said the US was taking the threats seriously and remained in close contact with South Korea.

The two Koreas have been technically in a state of war for six decades under an armistice that ended their 1950-53 conflict.

KCNA said the statement was issued jointly by the North's government, ruling party and other organisations.

There was no sign of unusual activity in the North's military or anything to suggest an imminent aggression, a South Korean defence ministry official said.

North Korea has been threatening to attack the South and US military bases almost on a daily basis since the beginning of March, when US and South Korean militaries started routine drills.

But the North has kept a joint industrial zone with the South running.

The Kaesong zone is a source of hard currency for the impoverished state and hundreds of South Korean workers and vehicles enter daily after crossing the heavily armed border between the rivals.

North Korean leader Kim Jong-un yesterday signed off on an order putting its missile units on standby to attack US military bases in the South and the Pacific, after the US flew two nuclear-capable stealth bombers over the Korean peninsula in a rare show of force.

US officials said the B2 bombers were on a diplomatic sortie aimed at reassuring allies South Korea and Japan and were also aimed at trying to nudge Pyongyang back to dialogue.

The South Korean government brushed off the North's latest statement, saying there was nothing fresh in it to cause greater alarm.

"North Korea's statement today is not a new threat but is the continuation of provocative threats," a ministry statement said.

The Defence Ministry urged the North to stop issuing threats, reiterating the position that annual military drills conducted jointly with US forces until the end of April were strictly defensive in nature.

The North's statement said it would respond "without mercy" to any action by the South that harmed its sovereignty.

In 2010, North Korea bombed a South Korean island close to the maritime border that Pyongyang disputes, killing two civilians and two soldiers and prompting the South to strike back with artillery and sharply elevating tensions.