The local currency was quoted at 1,063.0 against the dollar at the end of onshore trading, compared with 1,063.7 at the end of the Seoul session on Monday.
Dealers said trading was subdued throughout Tuesday with offshore players unwilling to make big bets. They suspected that local authorities may have bought at least $1 billion worth of dollars on Monday to slow the won's gains.
"Investors are generally playing it safe," one foreign bank dealer said, adding that the market lacked momentum.
The finance ministry and the Financial Supervisory Service, in separate statements released earlier on Tuesday, said they would step up monitoring of foreign exchange market activity following the won's rapid appreciation in recent months.
But analysts and dealers say that the won is likely to continue appreciating this year so long as the global economy improves as projected and monetary easing from major central banks continue.
The benchmark Korea Composite Stock Price Index ended down 0.7 percent at 1,997.94. Foreigners were net buyers of 50.0 billion won ($47 million) worth of local shares.
Local bonds rose on speculation that the Bank of Korea may deliver another rate cut at its policy meeting on Friday to boost growth. March futures on three-year treasury bonds ended up 0.07 points at 106.31.
Yields on the benchmark five-year treasury bonds and three-year treasury bonds each ended down two basis points from Monday's close.