Pompeo and Wang sounded calm with conciliatory remarks after their first face-to-face meeting that was held on the sidelines of the Association of Southeast Asian Nations (Asean) ministerial summit in the Thai capital.
Wang, who is also China's Foreign Minister, described the interaction as an opportunity to minimize differences between the two countries and work in areas of their mutual benefit, Efe news reported.
There was still room to expand "cooperation" in various areas between China and the US, he added.
In a Twitter post, Pompeo also sounded reconciliatory, saying he had "an in-depth exchange of views with Chinese State Councillor Wang Yi on US-China relations and North Korea, among other important topics of mutual concern".
"When it advances US interests, we are ready to cooperate with China," he added.
The US-China rivalry and an ongoing trade dispute between them are among the main focus points of the summit of the Foreign Ministers of the Asean groups and its allies.
"Look, we don't ever ask any Indo-Pacific nation to choose between countries," Pompeo said during a brief address at the start of his meeting with the Ministers of Asean member countries, comprising of Myanmar, Brunei, Cambodia, Philippines, Indonesia, Laos, Malaysia, Singapore, Thailand and Vietnam.
Several members of the Southeast Asian bloc maintain a dispute with Beijing over the sovereignty of a handful of islands and atolls in the South China Sea, a key strategic zone for trade routes that is rich in natural resources.
The US has repeatedly criticized Beijing's territorial claims in the region, and urged China in July to "cease its bullying behaviour" of sending Chinese frigates and warships to disputed waters.
Washington and Beijing are locked in a trade dispute since 2018 that has led to the implementation of tariffs on several products by both countries. The impact of the long-running trade war is already being felt on the global economy.
On Wednesday, US and Chinese negotiators concluded a brief round of talks the first after the Presidents of the two countries, Donald Trump and Xi Jinping, agreed to a new truce on the sidelines of the G20 summit at the end of June.
The Chinese state media described the Wednesday talks as "symbolic but harmonious". The White House, on the other hand, called the negotiations "positive".
( With inputs from IANS )