TAIPEI/BEIJING - Taiwan's defence ministry said on Wednesday that China had carried out another "joint combat readiness patrol" near the island, as Beijing said it would track down and punish "diehard" independence supporters wherever they are.

China, which views democratically governed Taiwan as its own territory, has made no secret of its dislike of President Lai Ching-te, whom it views as a "separatist", and staged two days of war games after he took office last month.

Last week, China threatened to execute "diehard" Taiwan independence separatists in extreme cases, a further ramping up of tensions that drew condemnation from Lai and his government, as well as the United States.

Taiwan's defence ministry said that starting at 7 a.m. (2300GMT) on Wednesday, it had detected 26 Chinese military aircraft, including J-16 fighters, operating to the north, centre and south of Taiwan, carrying out a "joint combat readiness patrol" with Chinese warships.

Taiwan frequently reports such missions, part of a pattern of what it says is Chinese harassment that has escalated in the past four years.

China's defence ministry did not immediately respond to a request for comment.

Speaking at a regular news briefing in Beijing, a spokesperson for China's Taiwan Affairs Office said the government had the legal right to protect the country's territorial integrity, defending last week's new guidelines to punish what Beijing views as separatism.

"National law enforcement and judicial organs will pursue all Taiwan independence diehards who test the law to the end no matter where they are and severely punish them in accordance with the law," Zhu Fenglian told reporters.

China will enforce "precision punishments", but the guidelines do not involve the majority of Taiwanese people, she added.

"The state punishes the crimes of secession and incitement to secession by 'Taiwan independence' diehards in accordance with the law. There is a solid legal foundation and sufficient legal basis for this," Zhu said.

Chinese courts have no jurisdiction in Taiwan and it is not clear how China could seek to enforce any judgements outside its borders.

Lai has repeatedly offered talks with China but been rebuffed. He rejects Beijing's sovereignty claims and says only Taiwan's people can decide their future.

(Reporting by Ben Blanchard and Ryan Woo; Editing by Muralikumar Anantharaman and Gerry Doyle)