South Korea's military says its air forces and the army have carried out a missile drill early in the day in response to North Korea's sixth nuclear test, adding the drills targeted the area where the test had been carried out.

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

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

North Korea conducted its sixth and most powerful nuclear test on Sunday, which it said was an advanced hydrogen bomb for a long-range missile, marking a dramatic escalation of Pyongyang's stand-off with the United States and its allies.

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Meanwhile, South Korea's environment ministry will announce on Monday its approval of an environmental assessment report for the deployment of the Terminal High Altitude Area Defense (THAAD) defense system in the country, a ministry official told Reuters.

South Korea said in June that it will hold off installing remaining components of the US defence system until it completes an assessment of its impact on the environment.

South Korea's President Moon Jae-in and Japanese Prime Minister Shinzo Abe have agreed to pursue stronger United Nations sanctions against North Korea after Pyongyang's sixth nuclear test a day earlier .

"Both heads of state agreed to cooperate closely with each other and the United States and shared the understanding there must be the most powerful sanctions and pressure applied on North Korea," presidential spokesman Park Su-hyun told a media briefing.

"And as part of that they agreed to push for more powerful UN sanctions," Park said after Moon and Abe spoke for about 20 minutes by phone.

The aim of stronger sanctions was to draw North Korea into dialogue, he said.

Earlier, US President Donald Trump and Prime Minister Abe condemned in a phone call North Korea's "continued destabilising and provocative actions," the White House said.

Trump also reaffirmed that Washington would defend itself and its allies "using the full range of diplomatic, conventional, and nuclear capabilities at our disposal," the White House said.

"The two leaders condemned North Korea's continued destabilising and provocative actions, confirmed the two countries' ironclad mutual defense commitments, and pledged to continue close cooperation," it said in a statement.

Key points:

• South Korea's President Moon Jae-in and Japanese Prime Minister Shinzo Abe agree to pursue stronger United Nations sanctions against North Korea.
• South Korea carries out military drills involving long-range air-to-surface missiles and ballistic missiles.
• UN Security Council convenes a meeting to discuss the situation.
• US Defense Secretary Jim Mattis warns North Korea that threats to the US and its allies "will be met with a massive military response" that will be both "effective and ovewhelming".
• US President Donald Trump condemns North Korea's "words and actions as "very hostile and dangerous" to the US on Twitter.
• North Korea on Sunday tests a hydrogen bomb designed for a long-range missile, marking a dramatic escalation in the global game of nuclear brinksmanship.