Meanwhile, Mattis confirmed that Washington will not be shooting down North Korean missiles unless they pose a direct threat to the US. Specific details, including when and how the aid would be offered, will be decided "with consideration of North-South relations", ministry officials had said.
South Korea has raised the possibility of reintroducing nuclear weapons to the peninsula.
As part of today's "routine" training exercise, USA jets few alongside four South Korean F-15K jet fighters to drop MK-82, MK-84 and GBU-32 bombs on stimulated targets at the Pilseung Range in Gangwon-do.
The secretary said the sanctions, which began in 2006, have shown North Korean leader Kim Jong Un that there's a penalty to pay for ignoring global concerns and norms.
"We must be willing to do more than to listen to our allies", the USA defense secretary said.
The secretary made a September 15 trip to Mexico City to strengthen the bilateral defense relationship and participate in Mexican Independence Day activities, and to the reporters he said that Mexico had declared the North Korean ambassador a persona non grata.
The UN Security Council unanimously passed a US-drafted resolution a week ago mandating tougher new sanctions against Pyongyang that included banning textile imports and capping crude and petrol supply.
Such tests were in violation of Security Council resolutions and showed that North Korea could now target the United States or Europe, he wrote.
Trump has vowed that North Korea will never be allowed to threaten the United States with a nuclear-tipped missile, but he has also asked China, North Korea's main ally and trading partner, to do more to rein in its neighbor.
"We will work with the global community to come up with a strong response toward North Korea ..."
"You see it as a primary effort of the United Nations General Assembly meetings going on this week in NY", he said.
Trump will make his first address to the United Nations on Tuesday and is expected to speak forcefully about the North Korean threat.
Mattis told Congress in June that any such war would be "more serious in terms of human suffering than anything we have seen since 1953", resulting in the "massive shelling" of Seoul while also putting Japan in harm's way.
Although any conflict on the Korean Peninsula would risk a wider conflagration, some officials in the administration of U.S. President Donald Trump have taken a harder line on the issue.
China has in the past been a key supporter of the North Korean communist regime, but that support may be dying out.
"So, yes, it's working", he said.
Nikki Haley, the U.S. Ambassador to the U.N., echoed those sentiments on CNN that same day, saying: "If North Korea keeps on with this reckless behavior, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed". Mattis confirmed that the USA would not shoot down a North Korean missile unless it poses a direct threat to the United States or its allies.
Four more of Japan's 34 PAC-3 units, largely used to defend the capital region, were relocated to southwestern Japan recently after North Korea warned of sending missiles toward the U.S. territory of Guam.