North Korean leader Kim Jong-Un called on his military to continue building up Pyongyang's nuclear force after issuing orders for the latest test-firing of ballistic missiles, the North's state media said Tuesday.

North Korea test-fired three missiles into the sea Monday, Seoul said, in a new show of force as world leaders met for the G20 summit in China.

"He stressed the need to continue making miraculous achievements in bolstering up the nuclear force one after another in this historic year," the official KCNA news agency said.

Kim was guiding a fire drill of his military aimed at checking the "capabilities of the units" and the accuracy of the "improved ballistic rockets deployed for action," it added.

Describing the combat performance of the rockets as "perfect", KCNA said Kim expressed "great satisfaction over the successful successive firing drill of ballistic rockets".

South Korea's defense ministry said the missiles were speculated to be Rodong missiles with a range of 1,000 kilometres (620 miles), and that they were fired without navigational warning to Japan.

"North Korea's ballistic missile launch is a direct violation of UN Security Council resolutions, aimed at showing off its nuclear and missile capabilities during the G20 summit," a ministry spokesman said in a statement.

The defence ministry in Tokyo said the three missiles were estimated to have fallen into Japan's maritime Exclusive Economic Zone.

"The ministry expresses serious concern over the missile launches as they pose a grave threat to Japan's national security," a ministry statement said.

The United States and Japan lodged a protest against Monday's test-firing and requested a meeting of the UN Security Council in New York.

The 15-member body will convene Tuesday and discuss whether the council will consider a response to the latest missile launches.

North Korea has conducted a series of missile tests this year in defiance of UN sanctions imposed after its fourth nuclear test in January.

Last month, it fired a submarine-launched ballistic missile from the northeastern port of Sinpo.

That missile flew 500 kilometres towards Japan, far exceeding the range of the North's previous sub-launched missiles.

Leader Kim Jong-Un described the August test as the "greatest success" and said it put the US mainland within striking range.

The launch was widely condemned by the US and other major powers, but analysts saw it as a clear step forward for North Korea's nuclear strike ambitions.