Mr Trump has been pressuring China, North Korea's benefactor, to help defuse the situation, but has also warned that the U.S. will settle the issue alone if other countries will not help.
The U.S. military says an aircraft carrier participating in curtailed training with Australia before starting its journey north toward the Korean Peninsula.
The rhetoric seems to be blurring the lines between North Korea and economic ties with China, issues that previous US administrations had kept separate.
But if Pyongyang is nervous that global sanctions are about to bite, it has not shown it, and senior officials have vowed to continue nuclear and ballistic missile tests. He called North Korea the most urgent and unsafe threat to the peace and security of the Asia-Pacific region.
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 also dedicated to the 105th birth anniversary of Kim Il-sung. He said the American commitment to South Korea is "iron-clad and immutable".
It's necessary to put pressure on North Korea so that it will accept dialogue in good faith.
U.S. Vice President Mike Pence is on board an American aircraft carrier stationed in Japan amid heightened tension on the Korean Peninsula. -South Korean military exercises now include training for precision strikes on the North's leadership or nuclear and military facilities.
Pence said, "We appreciate the challenging times in which the people of Japan live with increasing provocations from across the Sea of Japan". "We are with you 100 percent".
Ross has said he hopes to soon begin talks on a free trade agreement with Japan.
Pence made an unannounced visit to the Demilitarized Zone Monday at the start of his 10-day trip to Asia in a USA show of force that allowed the vice president to gaze at North Korean soldiers from afar and stare directly across a border marked by razor wire.
Later Monday, Pence reiterated in a joint statement alongside South Korean Acting President Hwang Kyo-ahn that "all options are on the table" to deal with threat and said any use of nuclear weapons by Pyongyang would be met with "an overwhelming and effective response".
Some see him as a hot-tempered, unpredictable leader who might attack North Korea before it masters the technology to build a nuclear-tipped missile that could hit the US mainland. Such statements by the 15-member council have to be agreed by consensus.
Chinese Foreign Minister Wang Yi on Tuesday made a new appeal calling for calm on the Korean peninsula.
While the US will continue to pursue diplomatic solutions, any conventional or nuclear attack by an enemy would be defeated "with an overwhelming and effective American response", Pence told the crowd aboard the ship Wednesday. "Of course I think that any country will feel that political diplomatic means are of course the first choice", Wang said.
U.S. Vice President Mike Pence, on a tour of Asian allies, has said repeatedly the "era of strategic patience" with North Korea is over.
The next step would be to bring home the 54,000 US troops stationed in Japan and another 25,000 troops in South Korea.
That kind of rhetoric has unnerved allies in Japan and South Korea, who would be at the sharp end of any North Korean response. Then, our government would follow its own Constitution and use our military for the only thing it is constitutionally authorized to do - provide for our own defense.