Relations between the two Koreas are at one of their lowest points, with diplomacy stalled and North Korean leader Kim Jong Un calling for increased weapons development, including tactical nuclear weapons.

"I remind the US military of the fact that the ever-increasing visibility of the deployment of the strategic nuclear submarine and other strategic assets may fall under the conditions of the use of nuclear weapons specified in the DPRK law on the nuclear force policy," Pyongyang's defence minister Kang Sun Nam said in a statement.

A White House official announced on Tuesday that a US nuclear-armed submarine was making a South Korean port call for the first time in four decades.

South Korea's President Yoon Suk Yeol, who has sought to boost ties between Seoul and Washington in the face of growing North Korean threats, visited the Ohio-class submarine Wednesday in southern Busan port.

Washington last deployed one of its nuclear-capable submarines to South Korea in 1981.

"The hostile forces posed the most undisguised and direct nuclear threat to the DPRK by bringing an Ohio-class strategic nuclear submarine to the Busan Port operation base, which means strategic nuclear weapons have been deployed on the Korean peninsula for the first time after 40 odd years," Kang said, referring to the North by its official name.

"The US military side should realize that its nuclear assets have entered extremely dangerous waters," he said in a statement carried by the official Korean Central News Agency.

Seoul and Washington have ramped up defence cooperation in response to Pyongyang's threats and repeated missile launches, staging joint military exercises with advanced stealth jets and US strategic assets.

They held the first Nuclear Consultative Group (NCG) meeting in Seoul on Tuesday, which aims to improve nuclear coordination and boost military readiness against North Korea.

- 'Direct, outright threat' -

Washington first announced it would deploy a submarine capable of launching ballistic missiles with nuclear warheads to the Korean peninsula in April, while South Korean President Yoon Suk Yeol was on a state visit.

North Korea baulks at having US nuclear assets deployed around the Korean peninsula.

"To the US and the 'ROK', any use of their military muscle against the DPRK will be their most miserable choice by which they will have no room to think of their existence again," Kang said.

North Korea's statement comes as an American soldier, Travis King, is believed to be in Pyongyang's custody after crossing the border during a tourist trip to the Joint Security Area in the Demilitarised Zone on Tuesday.

The US-led United Nations Command has said it is working with Pyongyang's military to "resolve this incident" but, with relations between Pyongyang and Washington at one of their lowest points in years, it's unclear what will happen.

Pyongyang has a long history of detaining Americans and using them as bargaining chips in bilateral ties.

Experts say it will be particularly difficult for Washington to seek consular access to King, with relations between the two countries at one of their most testy points in years.

In addition, nearly all foreign embassies in Pyongyang withdrew foreign staff after North Korea closed its borders in 2020 due to the Covid-19 pandemic.

That includes Sweden, which handles US consular affairs in the North Korean capital.