The Michigan is one of the largest submarines in the United States' arsenal and its tomahawk missiles have a range of 1,600km, meaning that from Busan the submarine could hit North Korean ports or military installations. The U.S. employs about 1,066,600 soldiers.
The warning comes as tensions ratcheted up between North Korea, its Asian neighbours and the US.
An official from Seoul's Defense Ministry couldn't confirm such details. "The council must be prepared to impose additional and stronger sanctions on North Korean nuclear and ballistic missile programmes".
"We agreed to warn North Korea to stop any additional strategic provocation and take intolerably strong punitive measures against Pyongyang if it goes ahead with such provocations", Kim Hong-kyun told reporters following his meeting with Joseph Yun of the USA and Japan's Kenji Kanasugi.
The meeting follows a meeting the US President held with ambassadors from United Nations member states on the security council on Monday where he emphasised US resolve to stop North Korea's progress.
While the USS Michigan arrived at the South Korean port of Busan for what was described as a routine visit to rest crew and load supplies, the U.S. is preparing for exercises with South Korea and Japan.
Trump was due to call Chinese President Xi Jinping after talking with Japanese Prime Minister Shinzo Abe earlier on Monday. Trump has been trying to get China to do more to bring its neighbor and ally into line, saying last week that he had "absolute confidence" that Xi could help solve the issue. "Cooperation with China and Russian Federation is the most important for effective pressure on North Korea", he said.
On Friday, Secretary of State Rex Tillerson will chair a special meeting of the U.N. Security Council.
The nuclear-powered submarine USS Michigan at Busan in South Korea on April 25.
Under Kim's leadership, North Korea has been aggressively pursuing a decades-long goal of putting a nuclear warhead on an ICBM capable of reaching the United States mainland.
Tillerson, along with Defense Secretary Jim Mattis, Director of National Intelligence Dan Coats and Joint Chiefs chairman General Joseph Dunford, would also hold a rare briefing for the entire US Senate on North Korea on Wednesday, Senate aides said.
Speaking in Sydney on Saturday, US Vice-President Mike Pence said the American aircraft carrier Carl Vinson would arrive in the Sea of Japan, bordering the Korean Peninsula, "in a matter of days".
The Global Times, a Chinese Communist Party-affiliated newspaper known for its nationalist views, said North Korea stands to lose the most in a conflict. Its state-run Rodong Simun newspaper touted the regime's ability to launch preemptive strikes on the South Korea-U.S. alliance with no advance notice if it spots a display of reckless behavior. Although, she says going the China route might be easier said than done.
To avoid that, the Trump administration is ramping up diplomatic efforts to put pressure on North Korea.
"North Korea's unlawful weapons programs represents a clear, grave threat to US national security", Pentagon spokesman Gary Ross said in a statement.
The timing of the port visit also was significant as North Korea marked army foundation day, one of its biggest holidays, on Tuesday. That statement did not directly follow with what was publicly stated by U.S. officials or by U.S. Pacific Command, which released a press statement noting the cancellation of a port visit for the Vinson in Australia.