South Korea has carried out a missile drill meant to "strongly warn" North Korea over its sixth nuclear test, military officials said.

The military training involved long-range air-to-surface missiles and ballistic missiles, South Korea's joint chiefs of staff said in a statement early on Monday.

The drill was carried out by only the Korean military, but more are being prepared with the US forces in South Korea, the statement said.

READ MORE: All the latest updates on the North Korea tensions

According to South Korea's state news agency, Yonhap, "the training came in response to the North's sixth nuclear test ... and involved the country's Hyunmoo ballistic missile and the F-15K fighter jets".

The military added that the target of the exercise was set considering the distance to where North Korea's test site was and the drill was aimed at practicing precision attacks and cutting off reinforcements.

North Korea conducted its sixth and most powerful nuclear test on Sunday, with what it said was an advanced hydrogen bomb for a long-range missile.

The test marks a dramatic escalation of Pyongyang's standoff with the United States and its allies.

The official Korean Central News Agency (KCNA) called the test a "perfect success".

'War should not be repeated'

Following the test, US President Donald Trump criticised South Korea for what he called its "talk of appeasement".

"South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing," Trump tweeted on Sunday.

South Korea responded by saying it would continue to push for the denuclearisation of North Korea through "peaceful means", Yonhap reported.

"Korea is a country that experienced a fratricidal war," Yonhap said, quoting a statement by South Korea's President Moon Jae-in's office.

"The destruction of war should not be repeated in this land."

Responding to the test earlier on Sunday, Moon vowed to push for the most powerful sanctions yet against North Korea at the UN Security Council in an effort to completely isolate it.

The Security Council is expected to meet on Monday.

The US also said it will launch a "massive military response" to any threat from North Korea.

"Any threat to the United States or its territories, including Guam, or our allies will be met with a massive military response, a response both effective and overwhelming," Secretary of Defense James Mattis told reporters on Sunday.