The milestone, which came for the first time since the country's stock market began trading some 70 years ago, was followed by gains on the Wall Street after U.S. President Donald Trump said he would not proceed with previously threatened tariffs on European countries, easing global trade uncertainty.
The rally expanded beyond semiconductors, with gains spreading to other major sectors. The junior KOSDAQ also rose 1.38 percent, reaching 964.40 by around 11 a.m.
Individuals bought a net 127.3 billion won ($86.8 million), joined by institutions with net purchases of 28.5 billion won, while foreign investors sold a net 202 billion won.
Among large-cap stocks, Samsung Electronics rose 3.81 percent to 153,200 won, SK hynix advanced 3.38 percent to 765,000 won, and LG Energy Solution gained 4.69 percent to 413,000 won. Samsung Life Insurance rose 1.6 percent to 177,500 won, while Samsung Biologics dropped 4.27 percent to 1,793,000 won.
Auto-related stocks were mixed, Hyundai Motor advanced 1.91 percent to 559,500 won, continuing its upward momentum, while Kia down 1.69 percent to 169,200 won in the early trade.
Defense and aerospace stocks declined, with Hanwha Aerospace down 0.99 percent at 1,302,000 won.
Shipbuilding-related shares weakened, with HD Hyundai Heavy Industries falling 2.54 percent to 615,000 won and Hanwha Ocean sliding 2.05 percent to 138,600 won.
Boosted by the KOSPI's historic milestone, the won strengthened, trading at 1,467.30 won per dollar.
Elsewhere in Asia, Japanese shares were higher, with the Nikkei 225 Index gaining 1.71 percent to 53,679.48. China's Shanghai Composite rose 0.39 percent to 4,132.97. Hong Kong shares also traded 0.25 percent higher at 26,651.26.
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