Tensions between Washington and Pyongyang have seen a recent upsurge, with US Vice President Mike Pence describing North Korea as "the most unsafe and urgent threat to peace and security" in the Asia-Pacific.
"Those who would challenge our resolve or our readiness should know: We will defeat any attack and meet any use of conventional or nuclear weapons with an overwhelming and effective American response".
The 1950-53 conflict between North, South Korea ended in a truce, not a peace treaty. "A trade deal with the US will be far better for them if they solve the North Korean problem!"
North Korea has unveiled a mocked-up video of an entire U.S. city being wiped out by a nuclear attack during a concert celebrating the birthday of founding father Kim Il Sung.
United States battleships were moved into the waters near the Korean peninsula as a precaution.
North Korean soldiers at a military training in March 2013.
Era of strategic patience with North Korea is over, says U.S. Vice President.
Amid heightened tension on the Korean peninsula, North Korea has escalated a war of words with the United States, warning of full-out nuclear war if Washington takes military action against it over its nuclear and missile ambitions.More news: Watch Lana Del Rey's New Video Lust for Life Featuring The Weeknd
Prior to Pence's arrival from South Korea, Abe on Monday called for increased diplomacy rather than the use of force in dealing with the current situation regarding tensions on the Korean Peninsula.
"Letting this dictator have that kind of power is not what civilised nations can allow to happen", he said referring to Kim.
"My hope is that they'll continue to get the message not just from the United States, here in Japan, and in South Korea, but on an increasing basis from China and countries all over the world committing to a denuclearized Korean Peninsula", he said.
But at the time of the announcements, the ships had temporarily headed in the opposite direction, to the Indian Ocean, for military exercises with Australia.
North Korea's state television aired footage of a choral performance attended by Kim Jong Un, the elder Kim's grandson, on Sunday, a day after a huge military parade in Pyongyang, which also marked the 105th birth anniversary of Kim Il Sung. Seoul, Tokyo, Honolulu and Guam are all now within range of North Korean ballistic missiles, and North Korea has threatened them with nuclear strikes.
"We can not help those who want to reach South Korea if a new regime does not guarantee the safety of North Korean defectors", it added.
Japan's ruling party recently urged the government to introduce advanced missile-defense equipment such as a land-based Aegis or Terminal High Altitude Area Defense (THAAD) system, which is being introduced in South Korea.