The currency was quoted at 1,074.2 against the dollar at the end of domestic trade, compared with 1,074.3 at the end of the Seoul session on Friday.
Dealers said market activity was subdued ahead of Christmas on Tuesday, when markets are closed. Monday's volume mostly consisted of real demand for the dollar or the won, they said.
"There's still expectations that the dollar will fall further against the won," said one dealer, adding that exporters were seen selling their dollars to convert their contract payments into won.
The showdown in Washington over a package of tax increases and spending cuts scheduled to take effect next year continues. No deal has been reached and negotiations won't resume until after Christmas, raising concern that a deal won't be reached until next year.
But investors refrained from taking large bets as the possibility of a last-minute bargain still remains. Dealers said the market would likely remain trapped in a narrow range until the year-end.
The benchmark Korea Composite Stock Price Index ended up 0.1 percent at 1,981.82. Foreigners were net buyers of 227.2 billion Korean won ($211.48 million) worth of shares.
Bonds fell on profit-taking pressures as investors expect economic indicators to improve in coming months, making a Bank of Korea rate cut less likely. March futures on three-year treasury bonds ended down 0.05 points at 105.82.
Yield on the benchmark five-year treasury bonds rose by one basis point, while yield on the three-year treasury bonds rose by two basis points.
Center>Copyright Reuters, 2012