The index closed at 5,084.85, up 2.73 percent from the previous session, and the junior KOSDAQ also rose 1.71 percent to 1,082.59 after reaching a milestone of 1,000 points the previous day for the first time in about four years.
Shares of Samsung Electronics rose 4.87 percent to 159,500 won, while SK hynix surged a whopping 8.70 percent to 800,000 won, further boosted by news that it was chosen as the exclusive supplier of HBM3E high-bandwidth memory for Microsoft's next-generation, artificial intelligence (AI) chip dubbed Maia 200.
Other large-cap stocks were mixed, with Samsung Biologics dropping 0.94 percent to 1,790,000 won, Samsung Life Insurance rising 2.69 percent to 187,100 won, and LG Energy Solution falling 1.8 percent to 408,500 won.
Shipbuilding-related shares were also mixed, with HD Hyundai Heavy Industries falling 2.81 percent to 588,000 won and Hanwha Ocean up 0.5 percent to 140,500 won.
Trump's threat somewhat affected auto-related stocks, as Hyundai Motor closed down 0.81 percent at 488,500 won, which was a slight recovery after falling nearly 5 percent in earlier trading. Kia also dropped 1.1 percent to 153,500 won.
Defense and aerospace stocks also traded lower, with Hanwha Aerospace down 2.54 percent at 1,230,000 won.
Individuals sold a net 1.02 trillion won ($705 million), while foreigners and institutional investors snapped up a net 850.8 billion won and 232.7 billion won, respectively.
The won remained stable against the greenback, trading at 1,444.60 per dollar.
Elsewhere in Asia, Japanese shares edged higher after opening lower, with the Nikkei 225 Index up 0.85 percent at 53,333.54.
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