• Both the U.S. and China won't want to see further violence and instability in Myanmar, said Scot Marciel, U.S. ambassador to Myanmar from 2016 to 2020.
• One way the U.S. and China could come together on the Myanmar issue is by supporting ASEAN, said Rizal Sukma of Center for Strategic and International Studies in Indonesia.
• Singapore's Foreign Minister Vivian Balakrishnan told CNBC on Monday that without national conversation and reconciliation, there wont's be progress in Myanmar.

U.S.-China relations may be off to a rough start under President Joe Biden, but the two countries could find common ground to work together to end the violence in Myanmar.

Scot Marciel, former U.S. ambassador to Myanmar, said both the U.S. and China wouldn't want to see escalating crisis in the Southeast Asian country.

A military coup on Feb. 1 triggered mass protests across Myanmar and security forces have tried to suppress the demonstrations through violent tactics. The crackdown has killed 780 people so far, while over 3,800 people are still detained, according to the Assistance Association for Political Prisoners advocacy group.

"My sense would be that this coup and certainly the turmoil and violence in Myanmar, I don't see how it's in China's interest ... my sense is China wants stability, for a whole host of reasons, so my guess is they're not thrilled with this, but they're being cautious," Marciel said Friday, during a webinar organized by Australian think tank Lowy Institute.  

"So, there may be some shared interests between United States and China in this, in certainly ending the violence and the instability," said Marciel, who was U.S. ambassador to Myanmar from 2016 to 2020.

The U.S. and other Western powers have strongly condemned the coup and imposed sanctions to pressure the military. Meanwhile, China's response has been more muted with Beijing emphasizing the importance of stability.

China is a major investor in Myanmar and shares a border with the Southeast Asian country. Some analysts have said that China's relatively subdued response could hurt its own interests.

Crisis not likely to resolve soon

One way the U.S. and China could come together on the Myanmar issue is by supporting the Association of Southeast Asian Nations (ASEAN), said Rizal Sukma, senior researcher at think tank Center for Strategic and International Studies in Indonesia, during the webinar.

The regional grouping held an emergency summit last month to address the spiraling violence in Myanmar. Its 10 member states subsequently released a statement that — among other things — called for the immediate end to the violence and appointment of a special envoy to mediate the crisis in Myanmar.

"ASEAN just hopes that whatever plan we're going to have on the ground in Myanmar, that the U.S. and China can also help to contribute to that plan, for example humanitarian assistance," said Sukma, who is a former Indonesian diplomat.

Sukma said he's "quite frustrated" that ASEAN has yet to appoint the special envoy to Myanmar two weeks after the statement. He said the regional grouping should "press ahead" with its plan so that it can start talking with the different parties with Myanmar.

Singapore's Foreign Minister Vivian Balakrishnan told CNBC's "Squawk Box Asia" Monday that it is up to the Myanmar military to decide how and when ASEAN can play a role.

Balakrishnan reiterated that the military must stop the violence and release political detainees — which include Aung San Suu Kyi and other democratically elected leaders. He said only then can "honest direct negotiations" between the army and civilian leaders proceed.

"Without this national conversation and reconciliation, you're not going to see any progress in Myanmar. Indeed the signs of a potential civil war are there," said the minister.

Marciel said he hopes the initiatives by the group can make "a little bit of headway" in Myanmar. But it's currently difficult to see the crisis resolving any time soon, and that likely means more suffering among the people, he added.

"It's really impossible to predict. I would say the most likely scenario over the next several months — which is as far as I can go — is sadly probably more of the same," he said. "I don't see the (military) giving in, I certainly don't see the people accepting this coup."