WATCH: Biden claims the US would defend Taiwan—White House walks it back

"China just tested a hypersonic missile. What will you do to keep up with them militarily and can you vow to protect Taiwan?"

"Yes and yes," the President answered.

We are," he paused, "militarily, China, Russia, and the rest of the world, we have the most powerful military in the history of the world. Don't worry that they're going to be more powerful. But what you do have to worry about is whether or not they're going to engage in activities that will put them a position where they may make a serious mistake.

"And so I have had, I have spoken and spent more time with Xi Jinping than any other leader has. That's why you have, y'know, you hear people saying, Biden wants to start a new cold war with China.

"I don't want a cold war with China, I just want China to understand that we are not going to step back, we are not going to change any of our views—"

Cooper interrupted. "So you're saying that the United States would come to Taiwan's defense if China attacked."

"Yes," Biden affirmed. "Yes, we have a commitment to do that," he said.

After this, the White House issued a statement to say that in fact there was no US policy change as regards Taiwan.

"There is no change in our policy," a spokesperson from the White House said, though they did not elaborate or say that Biden had misspoken, according to Reuters.

"The US defense relationship with Taiwan is guided by the Taiwan Relations Act. We will uphold our commitment under the Act, we will continue to support Taiwan's self-defense, and we will continue to oppose any unilateral changes to the status quo," the spokesperson said.

China was displeased with Biden's remarks, as they have been making their intentions as regards Taiwan known, with frequent incursions into Taiwanese airspace.

China cautioned the US "not to send the wrong signals to the forces of Taiwan independence, to avoid seriously harming Sino-U.S. ties and peace and stability in the Taiwan Strait," spokesman Wang Wenbin said in Beijing.

Taiwan has said that they would defend themselves against China, were they to attack. They have called on the world for help.

China published a three-stage plan for their potential invasion of Taiwan in July. China has declined to recognize Taiwanese independence ever since the communists took over the mainland in 1949. Taiwan has its own currency, government, military, diplomatic corps and passports. Anytime any nation or media outlet notes that Taiwan is its own nation, China balks and demands retractions.