The South Korean won ended local trade down 0.2 percent at 1,055.4 per dollar as offshore funds sold the currency and domestic importers bought the dollar for payments, traders said.
Investors became more wary that the foreign exchange authorities may intervene to stem the won's appreciation as it earlier rose as much as 0.3 percent to 1,050.6, its strongest since Jan. 2.
The South Korean currency jumped 1.5 percent last week when most other emerging Asian currencies slid.
On Monday, Indonesia's rupiah rose as Jakarta shares hit a 10-month high ahead of parliament elections later this week.
The Malaysian ringgit advanced as investors covered short positions on its overnight strength in non-deliverable forwards (NDFs).
U.S. employers added 192,000 payrolls in March, a notch lower than economists' median forecast and well down from some elevated expectations that had been made after a strong private jobs report.