"The U.S. will continue to pursue a constructive, results-oriented relationship with China, cooperation whenever possible will be the name of the game and competing vigorously where we must ... of course we recognize any sustainable Indo-Pacific order has a role for China", he said.
I believe China has more in common with Pacific Ocean nations, the United States and India than they have in common with Russian Federation.
Mattis on Saturday referred to that disinvitation as an "initial response" to China, but he did not outline any additional steps that may be taken.
The comments by Mr Mattis come at a time of increased tension between the two nations in the South China Sea and highlight how President Donald Trump's administration is looking to balance China's cooperation on North Korea while dealing with its activities in the disputed sea.
Speaking at an global security forum in Singapore, Mr Mattis rebuked China's military build-up in the disputed waters, warning of increasingly severe consequences should the rising Asian power fail to work collaboratively with neighbouring countries.
"Despite China's claims to the contrary, the placement of these weapon systems is tied directly to military use for the purposes of intimidation and coercion", Mattis said, according to Bloomberg News.
But he says the US welcomes cooperation with China wherever possible, and says he accepted Beijing's invitation to visit there soon.
U.S. Secretary of Defence Jim Mattis speaks at the IISS Shangri-la Dialogue in Singapore June 2, 2018.
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In January, Epic Games partnered up with Neowiz Games to release Fortnite in cafe-style businesses in South Korea. The suit specifically targeted Epic Games Korea and was filed in Seoul Central District Court.
Mattis responded that the question reflected a fundamental disconnect with the way worldwide tribunals have spoken on the matter.
"We did not do freedom of navigation for America alone, we do freedom of navigation, give freedom for all nations, large and small, that need to transit those waters for their own prosperity and they have every reason to do so", he said. Mr. Trump announced Friday that the nuclear-weapons summit he had canceled with North Korea's Kim Jong Un is back on.
Mr Mattis only made a glancing reference to North Korea, reiterating that it was a diplomatically led effort and the objective remained the "complete verifiable, and irreversible denuclearisation of the Korean Peninsula".
Gen Mattis said the issue of removing USA troops from South Korea was "not on the table" and that "our objective remains the complete, verifiable, and irreversible denuclearisation of the Korean peninsula".
Last week the USA withdrew an invitation for Beijing to participate the exercise known as Rim of the Pacific.
China believes islands, islets and other maritime features in the South China Sea are its sovereign territory and that it is within its rights to build defenses on them.
In a more conciliatory tone, Mattis said the U.S. would continue to pursue "cooperation whenever possible". The former Marine Corps general said Saturday that the deployment violated Chinese President Xi Jinping's commitments to not militarize the area.
Though much of the world is focused on an upcoming summit between North Korea and the United States, this year's Shangri-La Dialogue has focused primarily on the region's long-term future and how to deal with a more assertive China.