The three-day military drill, named “Joint Sword”, is intended as a “stern warning” to Taiwan, a self-ruled, democratic island that Beijing has pledged to annex one day.
Ms Tsai visited speaker Kevin McCarthy in Los Angeles on Wednesday, and the drills were announced on Saturday, soon after her return to the island.
Shi Yin, a spokesman for the People Liberation Army’s Eastern Theatre Command, described the operation as “necessary for safeguarding China's national sovereignty and territorial integrity".
In a statement, the PLA said it would deploy equipment and personnel into "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”.
According to AFP, a later report from state broadcaster CCTV said: "The task force will simultaneously organise patrols and advances around Taiwan island, shaping an all-round encirclement and deterrence posture."
The report went on to detail the type of weaponry China was putting through its paces, including "long-range rocket artillery, naval destroyers, missile boats, air force fighters, bombers, jammers and refuellers".
Exercises on Monday will include live-fire drills off the coast of China's Fujian province, which faces Taiwan, the local maritime authority said.
Taiwan's defence ministry said that by 4pm (0800 GMT) on Saturday that nine Chinese warships and 71 military aircraft had been detected around the island.
An earlier tally had already taken the number of daily aircraft crossings into Taiwan's southwestern air defence identification zone (ADIZ) past the highest in a single day this year, according to data collected by AFP.
Yet Ms Tsai remained undeterred. Hours after the announcement, she met foreign affairs committee chairman Michael McCaul and jointly denounced China.
At the meeting, she also stressed the importance of co-operation between the US and Taiwan. "Co-operation among democracies has become even more important. We will continue to work with the US and other like-minded countries to jointly defend the values of freedom and democracy," she said.
Mr McCaul oversees all US military sales to foreign nations and said Washington was working to quickly supply weapons to Taiwan. "We are doing everything we can in Congress to speed up these sales and get the weapons that you need to defend yourself, and we will provide training to your military, not for war, but for peace," he said.
China’s war games come just after Emmanuel Macron’s visit to Beijing for a high-level meeting on Ukraine, where the French President declined to comment on the Taiwan question. “I am neither Taiwan nor the USA. I am a good stoic, and I can only take care of the things that depend on me,” he said, according to Le Monde.
Taiwan’s defence ministry also released a video showing soldiers loading anti-aircraft missile launchers, fighter jets taking off, and other military preparedness exercises. The footage included surveillance of China's Shandong aircraft carrier, which sailed through waters south of Taiwan earlier this week.
The 75-second clip, which included English subtitles, ended with a caption saying: "We seek neither escalation nor conflict, but we remain steadfast, rational, and serious to react and defend our territory and sovereignty."