Confusion had clouded the carrier's whereabouts earlier this month after United States officials indicated it was sailing towards North Korea when in fact it was heading south.
Trump skipped calling Seoul during his phone conversations with his counterparts in Beijing and Tokyo on Sunday over the growing threat posed by North Korea's nuclear weapons and missiles program. The submarine arrived on the same day North Korea celebrates the anniversary of the founding of its military.
North Korea has ambitions to build a nuclear-tipped missile capable of reaching the United States mainland.
Meanwhile, the entire U.S. Senate has been invited to the White House for a briefing on Wednesday about the North Korea situation.White House Press Secretary Sean Spicer confirmed the upcoming briefing, for all 100 senators.
Trump on Monday urged the UN Security Council to consider stronger sanctions against Pyongyang, and United States senators will be briefed on North Korea at the White House on Wednesday.
The USS Michigan, a nuclear-powered submarine, arrived at the South Korean port of Busan in what was described as a routine visit to rest the crew and load supplies. South Korea's Yonhap news agency earlier said that the exercise involved 300 to 400 artillery pieces, but an official from Seoul's Defense Ministry couldn't confirm such details.
North Korea marked its most recent holiday, the 105th anniversary of the birth of North Korean founder Kim Il Sung, on April 15 with a massive military parade, a video featuring a simulated nuclear strike on an American city, and a missile test.
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.
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"When you have someone as unstable, seemingly, as Kim Jong Un, do you worry that words might force him into a catastrophic mistake?"
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.
Japan's Chief Cabinet Secretary Yoshide Suga told media that China's envoy for Korean affairs, Wu Dawei, would hold talks with Japanese Foreign Ministry officials.
A guided-missile submarine, it can carry up to 154 Tomahawk cruise missiles and is able to stealthily deploy up to 66 Navy SEALs or other special operations troops.
The main political event to mark the anniversary apparently was a "national meeting" held the day before, when thousands of senior military and civilian officials gathered at the People's Palace of Culture in Pyongyang.
Kim reported from Seoul, South Korea.
South Korea's Yonhap news agency reported that a former Korean-American professor was arrested at Pyongyang International Airport as he was attempting to leave the country.
He told the gathering: "The situation prevailing on the Korean Peninsula is so tense that a nuclear war may break out due to the frantic war drills of the US imperialists and their vassal forces for aggression".