"We maintain the capability to deter North Korea's most dangerous threats, but we also will back up our diplomats in a manner to keep this as long as possible in the diplomatic realm," Mattis said, responding to a question at the joint press briefing with India's Defence Minister Nirmala Sitharaman.
"Our goal is to solve this diplomatically. President (Donald) Trump is very clear about this issue," he added.
Yesterday, North Korea's Foreign Minister Ri Yong Ho told reporters at the United Nations that the Trump administration has declared war against North Korea and it has "every right" under the UN Charter to take countermeasures, "including the right to shoot down the United States' strategic bombers even if they are not yet inside the airspace border of our country".
His statement further spiked the tensions between the two countries.
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"We continue to maintain the diplomatically-led effort in the United Nations. You have seen unanimous United Nations Security Council resolutions passed that have increased the pressure, economic pressure and diplomatic pressure, on the North," he said.
Mattis also lauded efforts by India and some other countries to pressure North Korea over its "dangerous and destabilising" behaviour.
During Japanese Prime Minister Shinzo Abe's visit to India earlier this month, the two countries had denounced North Korea's nuclear programme as a grave threat to global peace and stressed on holding accountable all parties supporting the secretive nation's nuclear ambitions, in a veiled reference to Pakistan.