In his speech to the Shangri-La Dialogue, sponsored by the International Institute for Strategic Studies, Mattis sought to balance his hopeful comments on China with sharp criticism of what he called Beijing's disregard for international law by its "indisputable militarization" of artificial islands in disputed areas of the South China Sea.
In response, the Chinese foreign ministry said Beijing would "remain firm to defend its rights in the region".
But he made no mention of United States president Donald Trump's decision to pull the USA out of the Paris global climate change agreement, a move that infuriated allies far and wide. "I strongly support the USA position", Japanese Minister of Defence Tomomi Inada said during a speech at a regional security conference in Singapore.
Dean further touched on Washington's military buildup in different parts of the world, including near the Russian border. "What a crummy world if we all retreat inside our borders".
Haley urged all countries to break diplomatic ties with North Korea, stop illegal trade and do more to break up smuggling rings and cut off funding for the country's nuclear and missile programmes.
Though US military exercises in the Korean peninsula have been controversial in the global community, US Ambassador to the UN Nikki Haley urged security council members to enforce the new sanctions.
In his speech, Mattis acknowledged the hard diplomacy involved in getting China to act against North Korea, a longtime trade partner that shares a border.
Chinese U.N. Ambassador Liu Jieyi said that the resolution reiterated the importance of maintaining peace and security on the Korean Peninsula and northeast Asia.
The defense chief spoke directly to concerns that America might grant concessions to China in order to ensure its cooperation on North Korea, saying the issue was not "binary" and that the U.S. would continue to pressure Beijing elsewhere.
But she also said she was concerned about the situation in the South China Sea and in the East China Sea.
The North Korea's foreign ministry spokesman was quoted by KCNA news agency as responding to the United Nations' sanctions resolution.
Allies around the world have been concerned about the commitment of the United States since Trump took office on January 20 because of his "America First" rhetoric and expectations that he would concentrate on a domestic agenda. He added, however, that countries must "contribute sufficiently to their own security". "We must do more to build on the success of today's test to truly keep Americans and their allies safe from the threat of ballistic missile attack", said Mike Rogers (R-Alabama), chairman of the House Armed Service.
"We call on North Korea to refrain from provocative, destabilizing actions and rhetoric, and to make the strategic choice to fulfill its worldwide obligations and commitments and return to serious talks", State Department spokeswoman Anna Richey-Allen told Yonhap News Agency.