The index exceeded the 2,400-point mark, increasing for the third consecutive session.
Chipmakers continued to gain despite lingering valuation pressure.
"The Nasdaq and the KOSPI are going through a (price) adjustment process," Hana Financial Investment analyst Lee Jae-man said.
"Such adjustment is likely to come to an end, if the US Federal Reserve rolls out some concrete directions about the average inflation rate Thursday, and ensure the longevity of the current low-interest rate," he added.
Investor sentiment also improved as the South Korean government eased the social distancing level to Level 2 in the greater Seoul area Monday.
Large caps closed mixed in Seoul.
Market bellwether Samsung Electronics jumped 2.37 percent to 60,400 won, with No. 2 chipmaker SK hynix advancing 2.04 percent to 80,000 won.
Top pharmaceutical firm Samsung Biologics climbed 0.26 percent to 763,000 won, while Celltrion shed 0.84 percent to 296,000 won.
Internet portal giant Naver retreated 0.98 percent to 303,000 won, and its rival Kakao lost 1.45 percent to 373,500 won.
Leading chemical maker LG Chem gained 0.99 percent to 712,000 won, and rechargeable battery maker Samsung SDI gained 1.51 percent to 436,000 won.
The local currency closed at 1,183.5 won against the US dollar, up 3.4 won from the previous session's close.
Bond prices, which move inversely to yields, closed higher. The yield on three-year Treasurys lost 0.7 basis point to 0.919 percent, and the return on the benchmark five-year government bond fell 1.1 basis points to 1.217 percent. (Yonhap)