SINGAPORE (NYTIMES) - United States Defence Secretary James Mattis tried to lower the temperature on the array of hostilities between Washington and Beijing on Thursday (Oct 18), saying it is up to the militaries of the two competing global superpowers to act as a stabilising force amid rising political tensions.

During a 1½-hour meeting with his Chinese counterpart, Mr Mattis sanded down some of the sharp edges from Vice-President Mike Pence's pointed critique of China this month.

Mr Mattis urged the two militaries to talk through their many differences, and even repeated an invitation for General Wei Fenghe, China's Defence Minister, to visit the US, according to a senior Defence Department official who was in the meeting.

But the cordial tone belied deep tensions that showed no signs of abating on Thursday. China, as it usually does, brushed off Mr Mattis' complaints about Beijing's continued militarisation of disputed islands in the South China Sea.

Meanwhile, other countries present at a meeting in Singapore of South-east Asian nations continued to resist US entreaties to add their voices to the US challenge of China's claims in the disputed area.

And two of those countries - Malaysia and Thailand - even prepared for a joint naval exercise with China that US officials worry is part of a larger effort by Beijing to peel away US allies.

Mr Mattis, for his part, was hampered by the continued fallout and speculation from President Donald Trump's questioning on Sunday whether the defence chief would remain on the job, calling Mr Mattis "sort of a Democrat, if you want to know the truth", during an interview with CBS' 60 Minutes.

Mr Mattis later told reporters that Mr Trump had called him to reassure him that he was "100 per cent" behind the Defence Secretary, but in Asia, there has been speculation about how long Mr Mattis will be around.

The Mattis-Wei meeting comes as the US and China continue to lurch from one crisis to the next. Mr Trump accused China last month of meddling in the US midterm elections, an accusation Beijing rejected.

Mr Pence's Oct 4 speech has been widely viewed as foreshadowing a new Cold War between the US and China, and except for Mr Mattis, the Trump administration has only turned up the volume since.

On Wednesday, the White House said it planned to withdraw from a 144-year-old postal treaty that has allowed Chinese companies to ship small packages to the US at a discounted rate, part of a concerted push by Mr Trump to counter China's dominance and punish it for what the administration says is a pattern of unfair trade practices.

The military relationship that Mr Mattis is pushing as an island of stability is also taking hits.

Mr Mattis was supposed to begin his trip to Asia this week with a stop in Beijing for talks with Gen Wei, but China cancelled the visit, citing annoyance over sanctions Mr Trump imposed on a Chinese state military company for buying weapons from Russia, and Washington's plans to sell US$330 million (S$455 million) in military equipment to Taiwan, the self-governing island that Beijing claims as its own.

The biggest source of tension between the Pentagon and Beijing continues to be the South China Sea. China claims almost all the South China Sea, and strongly protests against US military patrols there.

The US, for its part, considers the sea to be international waters and sends bombers and warships through every so often to make that point.

During his talk with Gen Wei, Mr Mattis introduced a new dynamic into the standard talking points over the South China Sea issue, according to Mr Randall Schriver, the Pentagon's top official for Asia and the Pacific, who was in the meeting.

Mr Mattis sought to convey what he said were concerns of other Asia-Pacific countries over Chinese claims on the South China Sea.

"He talked about the reactions that he hears from other countries and their concern and confusion over China's actions not necessarily matching their words," Mr Schriver said.

US officials have recently started complaining privately that the US does the bulk of the naval work when it comes to overtly challenging China in the South China Sea, with numerous so-called Freedom of Navigation trips, during which US warships sail within 12 nautical miles of the disputed islands.

China always objects to the trips - last month a Chinese warship came within 41m of US naval destroyer Decatur as it conducted a Freedom of Navigation operation in the South China Sea.

The Pentagon characterised the manoeuvre as unsafe and unprofessional.

"When the Chinese ships are putting bumpers over the side," Mr Mattis told reporters on the plane at the beginning of his Asia trip. "You don't do that when you're out in the middle of the ocean, unless you're intending to run into something."

He vowed that US ships would continue to traverse what the US views as international waters.

But it is one thing for a US warship to challenge a Chinese one; it is a far bigger challenge for a smaller navy to do so.

Britain conducted a freedom of navigation operation in August - China complained about that too - but China's smaller Asian neighbours have been loath to follow suit.

During the meeting, Mr Mattis brought up the other countries.

"I think his point was that in some instances, other countries may not have the confidence, given China's strength, to always speak up," Mr Schriver told reporters after the meeting.

"But he wanted to let minister Wei know that he hears about it a great deal from other countries."

Mr Schriver acknowledged though, that for individual countries, "it's sovereign decisions on how they approach China bilaterally".