North Korea's military staged a "large-scale artillery drill" around the Wonsan region in the country's east on Tuesday, a statement from the South Korean military said.
The flurry of activity comes as North Korea marks the 85th anniversary of the founding of its army, a significant date in the country's calendar which raises the possibility of another North Korean nuclear or missile test.
So far, North Korea has remained silent about Kim's detention.
There was speculation that the North might carry out another nuclear or missile test.
In Pyongyang gas prices had spiked 73 per cent and gas stations were shutting, a day after long queues for gas were observed as North Koreans stocked up in anticipation of a new round of worldwide sanctions, Chinese media reported.
"It's been all about pressure and brinksmanship and military tools and tactics and chess something, and now to literally, directly taunt the leader of North Korea is like poking the hornet's nest yet again", said Paul Carroll, program director at the Ploughshares Fund, a group working to eliminate nuclear weapons.
South Korea says a USA nuclear-powered submarine has docked in the southern port of Busan, but it isn't expected to participate in joint naval exercises with South Korea.
South Korea's military says it's maintaining "firm readiness".
North Korea warned that the United States will have to choose between political and military surrender, according to the Yonhap report.
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North Korea's growing nuclear and missile threat is perhaps the most serious security challenge confronting US President Donald Trump.
The United States, Japan and South Korea agreed Tuesday to put maximum pressure on North Korea, the South's envoy for North Korea said after meeting his American and Japanese counterparts in Tokyo.
On Saturday, US citizen engaged in relief efforts in Pyongyang was detained attempting to leave North Korea, the third American to be arrested recently.
Despite the buildup, President Donald Trump has reportedly settled on a strategy that emphasizes increased pressure on North Korea with the help of China, the North's only major ally, instead of military options or trying to overthrow North Korea's government.
Kim said they discussed ways to get more cooperation from China and Russian Federation, which they agreed is crucial to applying effective pressure on North Korea to abandon its nuclear weapons program. "The council must be prepared to impose additional and stronger sanctions on North Korean nuclear and ballistic missile programmes".
Trump's comments come as the USS Michigan, one of US's most powerful submarines, arrived in South Korea in an apparent show of USA force and senators have also been summoned to the White House to be briefed Wednesday by top officials about the threat posed by North Korea.
Amid the military manoeuvrings, the White House has taken the unusual step of calling the entire US Senate in for a briefing on North Korea Wednesday afternoon.
President Donald Trump has said the USA was sending an "armada" to the Korean peninsula, including submarines.
Envoys from Japan, the USA and South Korea have gathered in Tokyo to discuss North Korea amid concern it may carry out another nuclear or missile test.