Washington — Taiwan's representative to the U.S. Alexander Yui said Sunday that "we want peace and stability" as Taiwan became among the most closely-watched issues in last week's summit between President Trump and Chinese President Xi Jinping. 

"We want to have our lives going on as usual. But we're not the ones creating all this trouble," Yui said on "Face the Nation with Margaret Brennan."

Mr. Trump returned from the summit in Beijing on Friday after two days of talks with Xi. Taiwan is central to China's interests, and Beijing has refused to rule out using military force to retake control. The U.S. has for decades has been committed to Taiwan's defense, but there's growing concern that could change under Mr. Trump. 

The pair "talked a lot about Taiwan" during the visit, Mr. Trump told reporters Friday aboard Air Force One. According to Chinese state media, Xi warned Mr. Trump of possible "clashes and even conflicts" if the Taiwan issue isn't "handled properly."

Yui said Sunday that while Mr. Trump heard "a lot about Taiwan" during the summit, "the problem is, he heard only their side of the story. He heard the Chinese story."

The ambassador said Taiwan would "love to tell our side of the story, the Taiwan story, which is one of resiliency, of staying up against the Chinese aggression."

"This has been going on for 77 years. This is not something that just happened when the DPP, the current ruling party of Taiwan, came to power," Yui said. "This has been going on for 77 years, since the inception of 1949 when they became a People's Republic. So this is not a recent thing." 

Yui expressed appreciation for the U.S.' approach in the Beijing summit, saying Mr. Trump and Secretary of State Marco Rubio were "very categorical with their visit to Beijing, publicly stating that there's no change in the United States' longstanding position in Taiwan."

While China wants the U.S. to stop weapons sales to Taiwan, Mr. Trump said he made "no commitment either way" and will "make a determination over the next fairly short period." He told Fox News after meeting with Xi that he views the pending weapons sale as a "very good negotiating chip."

"Taiwan would be very smart to cool it a little bit," Mr. Trump said. "China would be very smart to cool it a little bit.

"I think that's a statement of saying he wants status quo," Yui said, when asked about the statements. "That he wants no change in the Taiwan Straits, neither through economic or military coercion, and that the peace and stability of the Taiwan Straits is good for all parties concerned."

Asked whether Taiwan has an intention of declaring independence formally from China, Yui said what is meant by an emphasis on Taiwan independence is that "Taiwan is independent from the Chinese aggression."

"That we're not subordinate to the People's Republic of China in any way at all," he said. "And that's maintaining our sovereignty, our way of life, our democracy, our vibrant economy, our high-tech production. That is what is meant by independence. We are sovereign, independent, away from the People's Republic of China's attempt to swallow us as one of their own."

Yui stressed that Taiwan doesn't "want a war."

"It's like, our house, there's intruders trying to get into our house," he said. "We're trying to beef up our security system, and then they complain, the intruder complains, that because we're trying to improve our security system, it's making his job harder."