The military drills, which simulate the repulsion of an invading force, coincide with air-raid exercises across the island as it boosts combat preparedness in the face of rising military pressure from China.
Beijing's growing assertiveness towards the island it claims as its own, combined with Russia's invasion of Ukraine, have renewed debate about how to boost defence and prompted authorities to step up preparations in the event of a Chinese attack.
Beijing considers Taiwan to be part of its territory and has never renounced using force to bring the island under its control. Taiwan rejects Beijing's sovereignty claims and vows to defend its freedom and democracy.
As part of Taiwan's annual "Han Kuang" exercises, 20 warships including frigates and destroyers fired shells to intercept and attack a would-be invading force off Taiwan's northeast coast, while fleets of F-16 fighter jets and domestically manufactured Ching-kuo fighters launched air strikes.
Tsai, on board a decommissioned US Kidd class missile destroyer in waters off the port town of Suao on Tuesday, was seen wearing camouflage clothing and greeting soldiers.
"The excellent drill just now demonstrated the ability and determination by the soldiers of the Republic of China to defend the country," Tsai told soldiers via a cabin broadcast, using Taiwan's official name.
"Let's continue to guard our homeland together. Good job."
Chinese foreign ministry spokesman Zhao Lijian, asked about the drills at a regular briefing in Beijing, repeated China's warnings about any military moves by Taiwan.
"Taiwan's attempt to confront China militarily is akin to a mantis trying to obstruct a chariot," he said.
"In the end, it is doomed to fail."
The five-day drills come amid rising concerns about China's intentions towards Taiwan. China said on Monday it heightened warnings to the Biden administration about US House Speaker Nancy Pelosi's possible visit to Taiwan.
The United States does not have official diplomatic relations with Taiwan but is bound by US law to provide the democratically governed island with the means to defend itself.
