The drills - which Beijing has called a "stern warning" to the self-governing island - are a response to Taiwan's president visiting the US last week.
As the Chinese military simulated an encirclement of the island, the US urged China to show restraint.
Taiwan said at least 71 Chinese jets flew around the island on Saturday.
Taiwan also said 45 warplanes either crossed the Taiwan Strait median line - the unofficial dividing line between Taiwanese and Chinese territory - or flew into the south-western part of Taiwan's air defence identification zone.
Eleven Chinese ships were also spotted. The operation, dubbed "Joint Sword" by Beijing, will continue until Monday. Taiwanese officials have been enraged by the operation.
On Saturday defence officials in Taipei accused Beijing of using President Tsai's US visit as an "excuse to conduct military exercises, which has seriously undermined peace, stability and security in the region".
On day one of the drills, one of China's ships fired a round as it sailed near Pingtan island, China's closest point to Taiwan.
Taiwan's Ocean Affairs Council, which runs the Coast Guard, issued video footage showing one of its ships shadowing a Chinese warship, though did not provide a location.
In the footage a sailor can be heard telling the Chinese ship through a radio: "You are seriously harming regional peace, stability and security. Please immediately turn around and leave. If you continue to proceed we will take expulsion measures."
Other footage showed a Taiwanese warship, the Di Hua, accompanying the Coast Guard ship in what the Coast Guard officer calls a "standoff" with the Chinese vessel.
While the Chinese exercises ended by sundown on Saturday evening, defence officials in Taipei said fighter jet sorties started again early on Sunday morning.
US state department officials have urged China not to exploit President Tsai's US visit, and have called for "restraint and no change to the status quo".
A state department spokesperson said the US was "monitoring Beijing's actions closely" and insisted the US had "sufficient resources and capabilities in the region to ensure peace and stability and to meet our national security commitments".
The US severed diplomatic ties with Taipei in favour of Beijing in 1979, but it is bound by law to provide Taiwan with the means to defend itself.
US President Joe Biden has said on several occasion that the US would intervene if China attacked the island, but US messaging has been murky.
At Wednesday's meeting in California, Ms Tsai thanked US House Speaker Kevin McCarthy for America's "unwavering support", saying it helped "reassure the people of Taiwan that we are not isolated and we are not alone".
Mr McCarthy had originally planned to go to Taiwan himself, but opted instead to hold the meeting in California to avoid inflaming tensions with China.
Chinese state media said the military drills, which are due to run until Monday, would "simultaneously organise patrols and advances around Taiwan island, shaping an all-round encirclement and deterrence posture".
It added that "long-range rocket artillery, naval destroyers, missile boats, air force fighters, bombers, jammers and refuellers" had all been deployed by China's military.
But in Taiwan's capital Taipei, residents seemed unperturbed by China's latest manoeuvres.
"I think many Taiwanese have gotten used to it by now, the feeling is like, here we go again!" Jim Tsai said on Saturday.
Meanwhile, Michael Chuang said: "They [China] seems to like doing it, circling Taiwan like it's theirs. I am used to it now.
"If they invade we can't escape anyway. We'll see what the future holds and go from there."
Taiwan's status has been ambiguous since 1949, when the Chinese Civil War turned in favour of the Chinese Communist Party and the country's old ruling government retreated to the island.
Taiwan has since considered itself a sovereign state, with its own constitution and leaders. China sees it as a breakaway province that will eventually be brought under Beijing's control - by force if necessary.
China's President Xi Jinping has said "reunification" with Taiwan "must be fulfilled".
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