He cited as an example China's building of artificial islands and militarisation of facilities in worldwide waters in the South China Sea that undermined regional stability.
The danger of North Korea, anxiety of a coercive China and the threat of terrorism dominated talks between Australia and other regional countries at a security summit in Singapore over the past two days.
Responding to Tillerson's comments, China's foreign ministry urged "relevant countries" to support efforts by regional nations "to maintain peace and stability of the South China Sea, and play a constructive role in this regard rather than the opposite".
However, he cautioned that the United States can not accept Chinese activities that hurt the rules-based order that has benefited the region.
Continued US leadership in the region ensures "rules-based order" or freedom of navigation in the South China Sea, the defense chiefs said.
The U.N. Security Council on Friday unanimously adopted a US -drafted resolution imposing new targeted sanctions on a handful of North Korean officials and entities, in response to a series of ballistic missile tests this year that are banned under U.N. resolutions.
The Foreign Ministry added that Pyongyang "outrightly rejects the sanctions racket put forth by the United States and the UN Security Council to prevent the strengthening of our nuclear deterrence".
In another sign of increased pressure on North Korea, Japan's navy and air force began a three-day military exercise with two USA aircraft carriers in the Sea of Japan on Thursday.
Russia, who historically is often a deciding factor in security council votes, condemned DPRK behavior, but not without voicing continued disapproval of United States military muscle flexing against North Korea.
However, he reiterated the US' willingness to work closely with China diplomatically and economically, and to build a constructive, result-oriented and mutually beneficial relationship.
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Defense Secretary James Mattis reaffirmed US commitment to the Asian-Pacific region Saturday "based on strategic interests and on shared values".
"The regime's actions are manifestly illegal under global law", Mattis said.
In a stark contrast, North Korea said in a separate commentary issued through the Rodong Sinmun on Sunday that it was "unfazed" by U.S. President Donald Trump's North Korea policy of maximum pressure, adding "we will no longer fall for that old trick".
"Bear with us", Mattis said to a ballroom packed with defense ministers and military officers from at least 22 different countries.
But experts fear the tests indicate progress towards Pyongyang's ultimate goal of putting a nuclear warhead on a missile that could strike the continental US.
Citing last month's conclusion of a framework for a Code of Conduct between Asean and China to manage disputes in the South China Sea, and China's many bilateral and multilateral pacts, he said: "China can be said to be observing, supporting and safeguarding the worldwide and regional order".
He said while competition between the USA and China was bound to occur, "conflict is not inevitable".
Mattis called North Korea an "urgent military threat".
At the same time, the U.S. has been negotiating with China - North Korea's ally - to put more pressure on the secretive regime.
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