North Korean leader Kim Jong-un has promised bigger "gift packages" following Pyongyang's latest missile test, a statement that ratchets up already high tensions.

Kim supervised a new ballistic missile test on Monday, controlled by a precision guidance system, and ordered the development of more powerful strategic weapons to defend the country against the US, state media reported.

Kim said the reclusive state would develop more powerful weapons in multiple phases.

"He expressed the conviction that it would make a greater leap forward in this spirit to send a bigger 'gift package' to the Yankees" in retaliation for American military provocation, KCNA quoted Kim as saying.

The missile launched was equipped with an advanced automated pre-launch sequence compared with previous versions of the "Hwasong" rockets, North Korea's name for its Scud-class missiles, KCNA news agency said on Tuesday.

That indicated the North had launched a modified Scud-class missile, as South Korea's military has said.

The North's test launch of a short-range ballistic missile landed in the sea off its east coast and was the latest in a fast-paced series of missile tests defying international pressure and threats of more sanctions.

READ MORE: Japan to take action with US after N Korea missile test

South Korea said it had conducted a joint drill with a US supersonic B-1B Lancer bomber on Monday. North Korea's state media earlier accused the US of staging a drill to practise dropping nuclear bombs on the Korean Peninsula.

Drills planned

The US Navy said its aircraft carrier strike group, led by the USS Carl Vinson, also planned a drill with another US nuclear carrier, the USS Ronald Reagan, in waters near the Korean Peninsula.

A US Navy spokesman in South Korea did not give specific timing for the attack group's planned drill.

Florence Looi, reporting from Seoul, said North Korea accused the US and South Korea of military provocation and said this would bring the Korean Peninsula to the brink of war.

"South Korean media are also reporting that the [drill] took place just hours after North Korea conducted its missile launch, and reports have said that South Korean fighter jets have also been involved in the exercise. North Korea is not too happy about this," said Looi.

Monday's launch followed two successful tests of medium-to-long-range missiles in as many weeks by the North, which has been conducting such tests at an unprecedented pace in an effort to develop an intercontinental ballistic missile capable of hitting the mainland US.

Trump: North's 'great disrespect' for China

Such launches, and two nuclear tests since January 2016, have been conducted in defiance of US pressure, UN resolutions and the threat of more sanctions.

They also pose one of the greatest security challenges for US President Donald Trump, who portrayed the latest missile test as an affront to China.

"North Korea has shown great disrespect for their neighbour, China, by shooting off yet another ballistic missile ... but China is trying hard!" Trump said on Twitter.

READ MORE: Will China intervene in North Korea?

North Korea has claimed major advances with its rapid series of launches, claims that outside experts and officials believe may be at least partially true but are difficult to verify independently.

A South Korean military official said the North fired one missile on Monday, clarifying an earlier assessment that there may have been more than one launch.

The test was aimed at verifying a new type of precision guidance system and the reliability of a new mobile launch vehicle under different operational conditions, KCNA said.

However, South Korea's military and experts questioned the claim because the North had technical constraints, such as a lack of satellites, to operate a terminal-stage missile guidance system properly.