US Defence Secretary Mattis, who is on a two-day visit to India to strengthen military ties, said a United Nations resolution had increased pressure on the hermit nation.
He also said diplomatic efforts to tackle the crisis are continuing, but added the US would be able to tackle any attacks from Kim Jong-un.
Mr Mattis said: “We continue to maintain the diplomatically led efforts in the United Nations.
“You have seen unanimous UN security council resolutions passed that have increased the pressure on the North and at the same time we maintain the capability to deter North Korea’s most dangerous threats.”
Earlier today Russia warned of “catastrophic consequences” if a military conflict broke out on the Korean peninsula.
Russia hit out at America after US bomber jets were dispatched to South Korea, and slammed the approach as a “dead end”.
China echoed Russia’s concerns, and said war on the peninsula would have “no winners”.
The concerns come after President Trump was accused of declaring war on the secretive kingdom after he tweeted that North Korea “won’t be around much longer”.
North Korea’s Foreign Minister Ri Yong Ho responded by saying: “Last weekend Trump claimed that our leadership wouldn’t be around much longer and declared a war on our country.
“Since the United States declared war on our country, we will have every right to make all self-defensive counter measures, including the right to shoot down the United States strategic bombers at any time even when they are not yet inside the aerospace border of our country”.
White House press secretary Sarah Sanders said yesterday that the US has not declared war on North Korea, adding: “Frankly, the suggestion of that is absurd.”
She also said that it was “never appropriate” to shoot down another country’s aircraft in international waters.
Last week, in his first speech to the UN General Assembly, Mr Trump vowed to “totally destroy” North Korea if it continued to threaten the US and its allies.
This follows a war of words between Washington and Pyongyang where Donald Trump described Mr Kim and “rocket man”, and he in turn called The Donald a “mentally deranged person full of megalomania”.
Tensions between the two nations have been increasing over the last number of weeks, and intensified when Pyongyang conducted its sixth and largest nuclear test on 3 September. It has also threatened to test a hydrogen bomb over the Pacific.
Earlier this month, the UN Security Council unanimously adopted its ninth round of sanctions on Pyongyang in response to the nuclear test.