Dubbed "United Sharp Sword", the three-day operation will run until Monday, the People's Liberation Army's (PLA) Eastern Theatre Command said in a statement.
It will take place in "the maritime areas and air space of the Taiwan Strait, off the northern and southern coasts of the island, and to the island's east", said Shi Yin, a PLA front man, according to state news agency Xinhua.
China on Thursday began deploying warships around Taiwan. In the past 24 hours, three Chinese warships sailed through waters surrounding Taiwan, according to the island's defence ministry.
The exercise will also include live-fire drills on Monday off the coast of China's Fujian province, which faces Taiwan, the local maritime authority said in a statement.
missiles and fighter jets around Taiwan in its largest show of force in years, following a trip to the island by McCarthy's predecessor, Nancy
San Fran NanPelosi
Congresswoman-for-Life from the San Francisco Bay Area, born into a family of professional politicians. On-again-off-again Speaker of the House. It's not her fault when they lose, but it's her accomplishment when they win. Noted for her heavily botoxed grimace and occasional senior... uhhh... moments... Enjoying well-deserved retirement in Corleone, Sicily, or someplace like thatMcCarthy had originally planned to go to Taiwan himself. The decision to meet in Caliphornia, an impregnable bastion of the Democratic Party, instead was viewed as a compromise that would underscore support for Taiwan but avoid inflaming tensions with Beijing.
There were no immediate signs of heightened military activity on Pingtan, a southwestern Chinese island that is the closest point on the mainland to Taiwan.
A handful of cargo ships cruised through the waters near the coastline, while tourists in sunglasses and baseball caps snapped selfies on the viewing platforms.
But Fujian's provincial maritime authority has warned vessels not to enter waters near the live-fire drills on Monday.
Tsai returned to Taiwan on Friday after visiting her island's dwindling band of official diplomatic allies in Latin America, with two US stopovers that included meetings with McCarthy and other politicians.
"We let the international community see that Taiwan is more united when facing pressure and threats," she told news hounds, describing her trip as a success, adding: "We will never yield to suppression."
Hours before her meeting with McCarthy on Wednesday, China sent its Shandong aircraft carrier through Taiwan's southeastern waters on its way to the western Pacific.
Beijing said earlier Friday that "Taiwan is an inseparable part of China", after repeatedly warning against the Tsai-McCarthy meeting.
"China's illusory sovereignty and territorial integrity will never be divided," foreign ministry spokeswoman Mao Ning said at a regular press briefing.
"The future of Taiwan lies in reunification with the motherland."