The port call by the USS Michigan came as a USA aircraft carrier strike group steamed toward Korean waters and as top envoys for North Korea policy from South Korea, Japan and the United States met in Tokyo.
US President Donald Trump has called on the UN Security Council to impose tougher sanctions on North Korea to resolve the crisis.
Trump sent the USS Carl Vinson aircraft carrier strike group for exercises off the Korean peninsula as a warning to North Korea and a show of solidarity with US allies.
In this April 26 photo released by the U.S. Navy, the aircraft carrier USS Carl Vinson, foreground, transits the Philippine Sea with the Japan Maritime Self-Defense Force Atago-class guided-missile destroyer JS Ashigara, left, and the JMSDF Murasame-class destroyer JS Samidare.
Abe described his conversation with Trump as a "thorough exchange of views".
North Korea conducted a big live-fire exercise on Tuesday to mark the foundation of its military as a USA submarine docked in South Korea in a show of force amid growing concern over the North's nuclear and missile programmes.
"We will maintain close contact with the United States, keep a high level of vigilance and respond firmly", he said.
Trump has indicated he is willing to ramp up U.S. military pressure on North Korea while simultaneously encouraging China to use its influence on its ally, and reject bilateral diplomacy with Pyongyang.
Republican Sen. Lindsey Graham voiced confidence that Trump won't allow North Korea to reach that point.
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North Korea has conducted five nuclear tests and numerous missile tests, including one this month, a day before a summit between Trump and Xi in Florida. The government also states it will be impossible to determine what type of missile the rogue state has launched until it has struck, with the threat of nuclear or chemical warheads not ruled out.
But signaling that military action remains possible, Thornton has told a Washington think tank that the administration treats North Korea as its primary security challenge and is serious that "all options are on the table".
North Korea's drills coincided with military exercises held by US and South Korean navies in the Yellow Sea, off the western coast of the Korean Peninsula.
"Beijing sent a clear message to North Korean leader Kim Jong-un that a nuclear test would lead him to an impasse".
"As (North Korea has) one of the largest stockpiles of chemical weapons, again artillery can be used for that".
"This is a real threat to the world, whether we want to talk about it or not".
North Korea routinely accuses the United States of readying for an invasion, and threatens pre-emptive strikes to stop it.
"Judging from their recent words and deeds, policymakers in Pyongyang have seriously misread the United Nations sanctions, which are aimed at its nuclear/missile provocations, not its system or leadership", the newspaper said in an editorial.