The local currency was quoted at 1,110.7 against the dollar at the end of onshore trade, compared with 1,112.0 at the end of the Seoul session on Monday.
Dealers said the market was expecting some won demand from investors who were part of SK Telecom's block sale of roughly 440 billion won ($395.68 million) worth of Posco shares completed on Monday. Soem said at least a portion of the won demand may have materialised on Tuesday.
But other dealers said some dollar demand from local importers appeared to limit the won's gains. In the absence of firm leads, the won continued to trade within a narrow band.
South Korea and Japan earlier on Tuesday said they have mutually agreed to allow a $57 billion currency swap facility expire on Oct. 31, as the line was deemed no longer necessary to ensure financial market stability. The market shrugged off the news.
"Local market liquidity conditions remain healthy, so the expiration of the swap line won't have much of an effect," a local bank dealer said, adding that the won's exchange rate will likely remain stable for some time.
The benchmark Korea Composite Stock Price Index was down 0.1 percent at 1,979.04.
Local bonds were nearly flat as investors awaited the Bank of Korea's rate meeting on Thursday. A Reuters poll showed on Tuesday that the central bank is widely expected to cut rates for the second time in four months to shore up the sputtering economy.
December futures on three-year treasury bonds ended down 0.01 points at 106.34.
Yields on the benchmark five-year treasury bonds and the three-year treasury bonds were unchanged from Monday's close.