Following the talks, US officials said they sensed relations with China's military had stabilized, although the talks did not produce new agreements.
USA national security would suffer greatly without Defense Secretary Jim Mattis and several top Pentagon leaders slated to leave their posts next year, a key senator said Wednesday.
In a recent reminder of the risks amid rising tensions, the Pentagon this month accused China of an unsafe and unprofessional manoeuver in the South China Sea that brought a Chinese ship dangerously close to a U.S. Navy destroyer in worldwide waters.
"In order to maintain continuity in the Department of Defense, (Mattis') presence is going to be absolutely critical", the Rhode Island senator told reporters attending a breakfast roundtable at the Fairmont Washington DC Hotel Georgetown.
Gregory Poling, an Asia expert and fellow at the Center for Strategic and International Studies think-tank, said most countries in the region see Mattis as "a steady hand on the tiller".
"There was a commitment on both sides to try to find a time" for such a meeting, he added.
The pair had been due to meet earlier the month but Beijing cancelled the meeting, apparently in retaliation for Washington sanctioning a unit of China's military for buying Russian fighter jets and missiles in September.
Schriver said making military-to-military ties with China less brittle would be crucial to helping reduce the chances of a devastating conflict.
Wei and Mattis were in Singapore this week for an Association of Southeast Asian Nations.
Schriver said he believed that sentiment was shared by China's military, noting that it recently requested Thursday's talks in Singapore after Beijing decided against a planned Mattis-Wei meeting in China. Chinese military activity in the disputed areas is viewed by Washington as irresponsible while Beijing complains of an inappropriate US military presence.
Mattis, speaking to reporters as he flew to Asia this week, rejected Chinese claims that the United States was acting aggressively and pointed the finger at Beijing.
The talks took place as the US seeks to forge to more resilient military ties that can withstand mounting pressure between the world's two largest economies.
"We need to make sure that when we step on one another's toes it doesn't escalate into something that would be catastrophic", he said. "And the military relationship is to be a stabilizing force in the relations between the two countries".
"The (US) secretary making very clear we will continue to operate where global law allows", Schriver told reporters.
Military-to-military ties have always been one of the more fragile parts of the overall U.S.
Mattis's attempts to carve a better relationship with the Chinese military stands in contrast to the anti-Chinese rhetoric from the White House. That action was taken under the Countering America's Adversaries Through Sanctions Act passed by Congress in 2017. Earlier this month, a Chinese vessel had a naval altercation with a US destroyer near the highly disputed Spratly Islands.
Defence Minister Nirmala Sitharaman on Friday met US Defence Secretary James Mattis and her counterparts from the ASEAN, Japan and Australia, and discussed ways to strengthen bilateral and regional defence relations.
Beijing appears ready to normalise its interactions with the American military, a USA defence official said Wednesday, after relations soured during a sanctions spat and trade war.
Front and centre is China's military build-up in the South China Sea and its sweeping claims of sovereignty across the economically vital waters. Schriver noted that smaller nations like Vietnam, with limited naval and economic power, have reasons to express their concerns about China privately rather than in public.