US National Security Advisor Susan Rice brought the message during her latest visit, a source with the Foreign Ministry told China Daily on Wednesday.
"Rice spent roughly 70 percent of her time in meetings here discussing cooperation, and only 30 percent on other issues," said the source, who requested anonymity.
Rice was in China from Sunday to Wednesday, mainly to prepare for Obama's attendance at the G20 Leaders' Summit in Hangzhou, Zhejiang province, in September. She met with President Xi Jinping and other Chinese officials, including State Councilor Yang Jiechi.
The visit came amid tensions in the South China Sea after Beijing rejected a July 12 arbitration ruling in a case unilaterally brought by the Philippines over maritime disputes with China.
"Both sides agreed that we won't let disputes define the relations," the source said.
News releases issued by both sides afterward focused on bilateral cooperation, without directly mentioning the South China Sea issue.
However, the source said the two sides did discuss issues including the South China Sea and the advanced missile defense system that the United States and the Republic of Korea decided to deploy in the ROK, a move that has drawn strong opposition from China and Russia.
"We made our stances clear that the US should not cite the tribunal ruling on the South China Sea issue and that inappropriate handling of the THAAD anti-missile system will overshadow China-US relations," he said.
Rice spent a long time discussing anti-terrorism cooperation in meetings with Chinese officials, and she also touched on many other topics, including a bilateral investment treaty and military cooperation, he added.
"She also said that President Obama is glad to see a prosperous China, which is in the interests of the US, and that Washington is willing to work with Beijing to ensure a successful G20 summit," the source said.
Liu Youfa, former vice-president of the China Institute of International Studies, said, "Rice's remarks sent a signal to some Asian countries that the US-China relations are not only about the South China Sea.
"It is also a warning that these countries' plan to take advantage of conflicts between the US and China to seek their interests is unsustainable and shortsighted."
Jin Canrong, dean of the School of International Studies with Renmin University of China, said that US Secretary of State John Kerry took a similar low-profile stance on Monday while meeting with Foreign Minister Wang Yi at the ASEAN Foreign Ministers' Meeting.
"Washington has noticed the anger in China against the US on the South China Sea issue, not only from the government but also the ordinary people. They know that is not good for US interests."
