The United States has been deliberately ambiguous on whether it would defend Taiwan militarily.
But for decades it has sold weapons to Taipei to help ensure its self-defence, and offered political support.
Tsai met McCarthy outside Los Angeles on her way home from a visit with two allied countries in Central America.
In August last year, China deployed warships, 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 Pelosi.
Tsai meeting with McCarthy in the United States rather than in Taiwan, was viewed as a compromise that would underscore support for the island but avoid inflaming tensions with Beijing.
But China had repeatedly warned against any meeting, and began the latest wargames soon after Tsai returned to Taiwan.
“These operations serve as a stern warning against the collusion between separatist forces seeking ‘Taiwan independence’ and external forces and against their provocative activities,” Shi Yin, a PLA spokesman, said about “Joint Sword”.
Tsai responded to the drills by pledging to work with “the US and other like-minded countries” in the face of “continued authoritarian expansionism”.
LIVE-FIRE EXERCISES
The exercises on Monday were set to include live-fire drills off the rocky coast of China’s Fujian province, about 80km south of the Matsu islands and 190km from Taipei.
The local maritime authority said the exercises would be held between 7am and 8pm local time around Pingtan, a southeastern island that is China’s nearest point to Taiwan.