Mr Kim has repeatedly called to world to accept North Korea as a nuclear power.
The South Korean statement also quoted Trump as saying that an article in the Wall Street Journal newspaper saying that he was contemplating a military strike against North Korea was "completely wrong".
A fragile detente seems to have begun.
Mr Pence added that he will be sending a message to Kim Jong-un that the U.S. stands by South Korea when he accompanies USA athletes to the winter Olympics next month.
"In addition, we have provided materials to the North, which summarized the position of our side in relation to participation in the PyeongChang Winter Olympic Games and cultural events", the statement read. The U.S. has delayed scheduled military exercises until after the last gold medal is awarded. Splitting the Koreas along the 38th parallel was the idea of United States military planners to limit the influence of the Soviet Union and approved without a Korean presence at the 1945 Potsdam Conference.
US President Donald Trump has signalled that he has developed a "good relationship" with North Korean leader Kim Jong-un, despite tensions between them. Rex Tillerson, America's secretary of state, has said much the same. "It will fulfil our desires for a peace Olympics".
Diplomacy During Winter Olympics: A Permanent Solution Between Two Koreas?
But experienced Canadian coach Bruno Marcotte is in no doubt that if the promising duo do end up taking part in the February 9-25 Games in Pyeongchang, they will be fully deserving of their place. If the US resumes military exercises, North Korea may go back to testing missiles and bombs. Alternatively, Kim could choose to respond conventionally with thousands of rockets and artillery pieces, killing tens or hundreds of thousands of U.S., Japanese, and South Korean civilians and military personnel. "As a former steward of the nuclear launch keys, I've learned about the stability, competence and temperament it takes to hold such a responsibility, and Donald Trump has shown us all he possesses none of those qualities", he said. It was Ronald Reagan, who in his first year in office raised the possibility that the United States and the Soviet Union could survive an exchange of tactical nuclear weapons. There's no sign yet that it will, however. Kim is determined to make his country identify as nuclear state.
"We and our nation can not abide being hostages to the mood swings of a petulant and foolish commander-in-chief".
This approach is in contrast to President Trump's threats of war against the North if it continues on the path of repeated nuclear and missile tests.
North Korea boycotted the 1988 Summer Games in Seoul, meaning Pyeongchang will be the first Olympics they have attended in the South.
Who has blinked here? The mutual stand-down for the Olympics looks very much like the "freeze for freeze" approach that Russian Federation and China were recommending past year, although US officials resist the characterization. "Hopefully Kim Jong Un will find another path!"
After a year of hostile rhetoric, Mr Kim struck a warmer tone in his New Year's speech, when he signalled that a path to dialogue with Seoul was open, but he also boasted of the nuclear button on his desk.