The People's Liberation Army has launched joint air and sea patrols and military exercises around the island of Taiwan that aim to send a "severe warning" to "Taiwan independence" separatists.

The exercises were conducted after Taiwan's deputy head, Lai Ching-te, concluded a trip to Paraguay during which he made so-called "stopovers" in the United States and made remarks pursuing "Taiwan Independence".

The PLA's Eastern Theater Command announced on Saturday morning that it was holding the military exercises around the island, and that they would mainly focus on coordinating naval and air forces and seizing control of targets.

"It's a test for the theater's joint operation capacity in actual combat," said Senior Colonel Shi Yi, the command spokesman. He said the move is a severe warning for "Taiwan independence" separatists who have stepped up their collusion with foreign forces to make provocations.

The actions came after Lai made "stopovers" in New York and San Francisco, both on his way from Taiwan and back during the trip to Paraguay.

While in Paraguay, Lai, who is also a 2024 leadership candidate for the ruling Democratic Progressive Party in Taiwan, spoke with US Interior Secretary Deb Haaland, who led the US delegation attending the inauguration of Paraguayan President Santiago Pena.

In a separate statement released later on Saturday, the spokesman said the command carried out joint training in waters and airspace north and southwest of the island to cover the seizure of maritime and air control, as well as anti-submarine exercises to test the abilities of coordinated combat.

In addition, the command posted several videos on Saturday of the joint patrols and military exercises near Taiwan on its WeChat account.

As shown in the videos, the command's naval forces dispatched several destroyers, frigates and missile boats. Meanwhile, fighter planes, early warning aircraft and jamming aircraft took off, and the command's Rocket Force troops were quickly mobilized.

According to the command, the forces have approached targets from multiple angles for a long period of time, "shaping a deterrent posture" toward the island.

The command also released a video showing one of its warships approaching a warship of Taiwan. In another video, there is a poster that elaborates China's position on the Taiwan question, with the statement that "the one-China principle is the bottom line that cannot be crossed" highlighted.

In a description of a video, the command said that "ready to fight at any time, the troops of the Eastern Theater Command will resolutely defend national sovereignty and territorial integrity". The command also stressed in a video on Sunday that "when national dignity and the reunification of the motherland are challenged, the PLA is the patron saint of eternal peace".

Zhong Houtao, an associate professor at the University of International Relations in Beijing, said Beijing is sending a strong signal that it has zero tolerance toward "Taiwan independence" separatist forces and their collusion with external forces. He referred to both the military action and an announcement by the Ministry of Commerce that it would study the suspension or partial suspension of tariff preferences for Taiwan products under the Economic Cooperation Framework Agreement.

In a statement on Saturday, the Taiwan Work Office of the Communist Party of China Central Committee strongly condemned Lai for relying on the US to seek "independence" of the island without scruple.

Lai has made frequent remarks seeking "independence" to create cross-Strait confrontations, and has advocated preparing for war, and his so-called transit in the US this time was for his own votes, the statement said.

The office said that Lai's acts proved that he is a complete worker for "Taiwan independence" and a troublemaker through and through who will only bring Taiwan to the danger of war.

"We are willing to create conditions for peaceful reunification but will never allow any separatist actions for 'Taiwan independence'," it said.

The office urged the US to abide by the one-China principle and the three Sino-US joint communiques, and deal with the Taiwan question in a prudent way.

"No one and no force should underestimate the strong resolve, firm will and strong ability of the Chinese government and people to safeguard national sovereignty and territorial integrity," it said.

Cui Jia contributed to this story.