The KOSPI on April 28 closed above the 6,600 level for the first time ever on a closing basis, setting a record high. Institutional buying drove the index higher.

The KOSPI ended up 25.99 points, or 0.39 percent, at 6,641.02. The index opened up 31.77 points, or 0.48 percent, at 6,646.80 from the previous session and kept its gains to close higher for a second straight day.

At one point during the session, it rose as high as 6,712.73, also breaking above 6,700.

By investor type, individuals net sold 130.4 billion won and foreigners net sold 184.5 billion won. Institutions net bought 351.2 billion won, leading the index.

Top market-cap stocks were mixed. Samsung Electronics fell 1.11 percent to 222,000 won, while SK Hynix rose 0.62 percent to 1,300,000 won.

Hyundai Motor jumped 5.92 percent to lead gains. SK Square, up 2.79 percent, and LG Energy Solution, up 1.72 percent, also ended higher.

Hanwha Aerospace fell 4.06 percent, Doosan Enerbility slipped 0.85 percent, HD Hyundai Heavy Industries lost 0.89 percent and Samsung Biologics fell 0.33 percent.

The Kosdaq ended down 9.06 points, or 0.74 percent, at 1,217.12.

In Seoul's foreign exchange market, the won stood at 1,473.20 per dollar, up 1.80 won from the previous session.