Taiwan is pushing back hard after Beijing attacked President Lai Ching-te's National Day speech, a sign that cross-strait tensions are rising again rather than easing.

• Taiwan's foreign ministry said the Republic of China (Taiwan) and the People's Republic of China exist as equals and neither is subordinate to the other.
• Beijing's Taiwan Affairs Office repeated the "one China" principle and called Lai's speech a distortion of the facts.
• Taipei insists only Taiwan's 23 million people can decide the island's future, and that China has no say in it.
• The ministry called on Beijing to stop hostile attacks that raise the risk of confrontation and to drop the use of force or coercion to change the status quo.
• Taiwan says it will keep working with democratic partners abroad to defend its sovereignty and keep the region stable.

Outlook: Expect more sharp words from both capitals in the coming weeks, with no sign either side will soften its position.