The complex relationship between the United States and China has consistently been a focal point in global geopolitics, marked by periods of cooperation and rivalry. With Donald Trump's potential return to the political landscape, a new chapter in this intricate narrative could unfold. In this context, China has expressed its approach to future interactions with the US, emphasizing a commitment to manage relations with "mutual respect."

The dynamic between the US and China has been multifaceted, influenced by various economic, political, and military dimensions. During Trump's previous presidency, the relationship was notably strained, characterized by a trade war, technological competition, and disputes over issues like intellectual property and regional security in the South China Sea.

China's stance, articulated by Foreign Ministry spokeswoman Mao Ning, suggests a readiness to cooperate with the US but within a framework that acknowledges mutual respect. This implies a recognition of each nation's sovereignty and interests, a critical element in navigating the competitive aspects of their bilateral relations.

Under Trump's earlier administration, the US took a more confrontational approach towards China, seeking to alter trade balances and limit China's growing influence on the global stage. This period saw significant tariffs imposed on Chinese goods and efforts to restrict Chinese technology companies’ operations in the US. These actions not only affected economic conditions but also intensified diplomatic tensions.

Despite these past challenges, both nations are aware of the necessity for dialogue and collaboration on global issues such as climate change, pandemic responses, and maintaining international financial stability. This recognition forms the basis of China's declared willingness to engage with the US in a mutually respectful manner.

Yet, the expectation remains that political and economic rivalry will persist, especially if Trump leads the US again. The ongoing technological race, particularly in areas like 5G and artificial intelligence, underscores this competitive spirit. Both countries are vying for leadership in innovation, which is seen as essential for securing economic and military advantages in the 21st century.

In conclusion, while China has signaled a cooperative attitude grounded in mutual respect, the underlying competitive dynamics are likely to continue influencing US-China relations. This balance of cooperation and rivalry will play a crucial role in shaping not only bilateral interactions but also broader global stability and progress as the two superpowers navigate this new phase in their relationship.