TAIPEI—China sent several dozen military aircraft on sorties near Taiwan, launching its largest such show of aerial force in months as two U.S. aircraft carrier strike groups concluded training exercises with Japan in the region over the weekend.

China’s People’s Liberation Army on Sunday sent a total of 39 warplanes—including two dozen J-16 fighter jets and a nuclear-capable H-6 bomber—near Taiwan’s airspace, according to the Taiwan Air Force. The flurry of Chinese sorties was the most intense since the PLA sent a record 56 aircraft near the democratically self-ruled island on Oct. 4.