Pentagon official Randall Schriver told reporters after the longer-than-expected 90-minute meeting that Mattis "repeated our desire for a durable relationship that is a stabilizing force in the overall relationship".
Asked at a press conference about the usefulness of such non-binding protocols in the light of a recent near-miss between a USA warship and a Chinese destroyer in the South China Sea, Defence Minister Ng Eng Hen likened the guidelines to seat belts in vehicles.
On Thursday, alongside the Wei-Mattis meeting, China's foreign ministry spokesman Lu Kang said Beijing was "verifying the situation", but reiterated it would take "resolute measures when necessary to defend our sovereignty and security interests".
Wei has a standing invitation to visit the United States but no date was agreed for his trip, Schriver said.
"We will fly sail and operate where worldwide law allows but we are also looking for partners to give voice to keeping. global law. upheld".
The leaders of the ten-nation Association of Southeast Asian Nations (ASEAN) grouping signed the joint declaration following a meeting in Singapore.
Military-to-military ties have always been one of the more fragile parts of the overall U.S.
President Donald Trump has frequently assailed China over its economic policies and earlier this month, US Vice President Mike Pence issued a litany of complaints, accusing Beijing of "predatory" trade practices and military "aggression", among other charges.
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The Pentagon chief met Thursday with his Chinese counterpart, General Wei Fenghe, on the sidelines of the gathering as they sought to normalise military relations that have dramatically soured over trade and sanctions tensions.
Speaking to reporters traveling with him earlier this week, Mattis acknowledged that the relationship has been hard in recent times.
The 10 ministers are hoping to convince the partner-countries of ADMM-Plus - Australia, China, India, Japan, New Zealand, South Korea, Russia, and the U.S. - to sign on to the air code, as they did with Cues at last year's meeting.
The ASEAN ministers applauded the participation of the US and China as their partners at the ADMM, saying that the US-China relationship plays an important role in regional peace and stability.
Beijing's expansive claims to the South China Sea have always been a source of friction with rival claimants in Southeast Asia, as well as the U.S. which has traditionally been the dominant naval power in the area.
"They do face potential risk angering China".
At Friday's meeting, Mattis stressed that "no single nation can rewrite the global rules of the road, and we expect all nations - large and small - to respect those rules".
The air guidelines - a set of communication protocols called Game (Guidelines for Air Military Encounters) - are meant to reduce the likelihood of accidents that could escalate into a conflict, especially with increased air traffic in the region.