South Korea and the United States wrapped up their annual large-scale military drills on Sunday but continued a separate joint naval exercise that has triggered the threat of nuclear war from North Korea.

The USS Carl Vinson aircraft carrier group arrived in waters near the Korean Peninsula and began exercises with the South Korean navy late on Saturday. The South Korean navy declined to say when the exercises would be completed.

North Korea has threatened to sink the US armada.

Tensions on the Korean Peninsula have been running sky-high for weeks, with signs the North might be preparing a sixth nuclear weapon test - and with Washington refusing to rule out a military strike in response.

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The massive Foal Eagle military exercises - which the defence ministry in Seoul said ended as scheduled on Sunday - involved about 20,000 South Korean and 10,000 US troops. Another annual joint manoeuvre known as Key Resolve ended last month.

Both play out scenarios for a conflict with North Korea, but Seoul and Washington insist they are purely defensive in nature. Pyongyang says the drills are provocative plans for an invasion or a "decapitation strike" against the North Korean leadership.

A North Korean state-run newspaper on Sunday warned of "catastrophic consequences", accusing the USS Carl Vinson strike force of rehearsing a "pre-emptive attack on the North" in a "special operation".

"This has pushed the tense situation on the Korean Peninsula to an unpredictable dangerous phase," said the state-run North Korean newspaper Minju Choson in a commentary.

"The enemies have to know that military threat and blackmail with the mobilisation of nuclear carriers and nuclear submarines cannot work on the DPRK," it said, using the acronym for the Democratic People's Republic of Korea.

"The US and the puppet group of traitors have to ponder over the catastrophic consequences to be entailed by their foolish military provocation - and stop running wild."

US President Donald Trump has warned of a possible "major conflict" after Pyongyang carried out a series of failed missile tests, including one on Saturday.

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North Korean ballistic missile tests are banned by the United Nations because they are seen as part of Pyongyang's push for a nuclear-tipped weapon that can hit the US mainland.

Trump said North Korean leader Kim Jong-un will eventually develop better missiles, and "we can't allow it to happen".

In a taped interview broadcast on Sunday on the US network CBS, the president would not discuss the possibility of military action, saying: "It is a chess game. I just don't want people to know what my thinking is."

Trump will speak with the leaders of Singapore and Thailand on Sunday over the "potential for nuclear and massive destruction in Asia", because of the situation with North Korea, White House Chief of Staff Reince Priebus said.

"There is nothing right now facing this country and facing the region that is a bigger threat than what is happening in North Korea," he said.

The US and South Korea started installing a missile defence system that is supposed to be partially operational within days.

The Terminal High-Altitude Area Defence system, or THAAD, is controversial in South Korea. Residents in the county of Seongju, where the missile system is being deployed, scuffled with police on Sunday.

Trump raised eyebrows in South Korea last week when he said would make Seoul pay $1bn for the missile system. His national security adviser, HR McMaster, said on Sunday the matter is subject to negotiation.