South Korea's Yonhap news agency earlier said that the exercise involved 300 to 400 artillery pieces and that North Korean leader Kim Jong Un likely observed what was one of the country's largest artillery drills.
Nikki Haley, the USA ambassador to the United Nations, isn't ruling out a US strike against North Korea if Pyongyang tests another nuclear missile.
Tuesday marks the 85th anniversary of the founding of North Korea's military, a significant date in the country's calendar.
North Korea's leader Kim Jong Un did not attend.
Tensions have soared in recent months as it carried out a string of missile tests that sparked tit-for-tat sabre-rattling between it and Washington.
A North Korean foreign ministry spokesman said those meetings called by USA officials clearly reflected the United States pressure that could "ignite a full-out war" on the Korean peninsula.
"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.
Trump's statements came as the USS Michigan arrived at a South Korean port Tuesday, in the city of Busan.
Although vague about what course of action Washington might pursue in Kim's case, Haley said it is looking to China to maintain pressure on North Korea.
On Saturday, US citizen engaged in relief efforts in Pyongyang was detained attempting to leave North Korea, the third American to be arrested recently.
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South Korea's envoy Kim Hong-kyun wouldn't give details, but said it would include stronger enforcement of United Nations Security Council resolutions, and country-level sanctions.
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 says the envoys strongly denounce North Korea's continuing provocations, including threats of a nuclear war.
Kim said the roles of China and Russian Federation are crucial to apply pressure effectively on North Korea toward its denuclearization.
Tension on the Korean Peninsula was high on the anniversary, with US and South Korean missile destroyers also due to hold a live-fire exercise in the western sea on the North Korean border. He said they also recognized China's recent steps toward that goal.
Trump told ambassadors from U.N. Security Council member countries that they must be prepared to impose additional and stronger sanctions on North Korea.
Japan's Foreign Ministry announced that China's envoy for North Korea, Wu Dawei, was arriving in Tokyo on Tuesday for talks with Kanasugi that may take place later this week.
South Korean newspapers are questioning whether President Donald Trump is tuning out South Korea as he shapes his North Korea strategy.
Joseph Yun, US Special Representative on North Korea policy, said he discussed American policy to "enhance pressure" on the North "because we really do not believe that North Korea is ready to engage us towards denuclearisation".