He said the USA and its allies will achieve its objectives through "peaceable means or ultimately by whatever means are necessary" to protect Seoul and stabilize the region.
"But the era of strategic patience is over", he declared.
Deputy national security adviser K.T. MacFarland told Fox News' Chris Wallace on "Fox News Sunday" that North Korea was a problem for everybody in the region, including China - the North's strongest ally.
"Just in the past two weeks, the world witnessed the strength and resolve of our new president in actions taken in Syria and Afghanistan".
McMaster added that the United States is working with its allies, the Chinese authorities to develop a range of options to deal with North Korea.
And I think there is worldwide consensus now, including the Chinese, and the Chinese leadership, that this is a situation that just can't continue.
The US, which stations 28,500 troops in South Korea, would "defeat any attack and we will meet any use of conventional or nuclear weapons with an overwhelming and effective response".
US Vice-President Mike Pence has declared that his country's "era of strategic patience" with North Korea is over.
Most options fall into four categories: economic sanctions, covert action, diplomatic negotiations and military force.
While Washington had a "wide array of tools" at the president's disposal, "for this particular case, if they (North Korea) took the time and energy to launch a missile that failed, we don't need to expend any resources against that".
We highlighted earlier Saturday North Korea's annual celebration of its founder Kim Il Sung and the exhibition of a long line of missiles through the streets of Pyongyang.
USA prepared to 'utterly destroy' N Korea nuclear sites
In February, Trump told China's President Xi Jinping that the U.S. would, in fact, honor the decades-old policy. Recent satellite imagery suggests the country could conduct another underground nuclear test at any time.
The North has a habit of firing off missiles to mark major political anniversaries, or as gestures of defiance to top USA officials visiting the region.
Tensions have risen as Trump takes a hard rhetorical line with Kim Jong Un, who has rebuffed admonitions from China and proceeded with nuclear and missile programmes seen by Washington as a direct threat. Meanwhile, President Trump has been in talks with Chinese President Xi Jinping to pressure North Korea to stop its provocations.
While China has reportedly suspended package tours to North Korea, British travel company Koryo Tours said it would keep sending tourists to the North.
Liberal Democrat leader Tim Farron said Prime Minister Theresa May and Johnson needed to use what influence they had with Trump to tell him that "aircraft carrier diplomacy" was not the answer.
China is the largest source of the US trade deficit, and Trump has previously criticized China for unfairly devaluing its currency to give it an unfair competitive advantage in global markets.
Defence Secretary Sir Michael Fallon has been briefed by his United States equivalent General James Mattis on American options for dealing with North Korea in recent weeks, The Sunday Times said. While the North did not conduct a nuclear test, the specter of a potential test and an escalated US response has trailed Pence as he undertakes his Asian tour.
Japanese Prime Minister Shinzo Abe urged North Korea on Monday to refrain from taking further provocative actions, comply with United Nations resolutions and abandon its nuclear missile development.
"The people of North Korea, the military of North Korea should not mistake the resolve of the United States of America to stand with our allies".
North Korea's actions come as tensions on the Korean Peninsula have spiked.
According to the adviser, the test had been expected and the US had good intelligence both before and after the launch.
He arrived amid rising tensions between the USA and North Korea over its nuclear weapons program. Overall imports from North Korea to China, however, have increased.
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