Greek civil servants threatened on Monday to stage more strikes in protest at government austerity measures, further fuelling market concerns over fiscally fragile euro zone members and weighing on the single currency and bonds.
Tokyo traders said it would not be easy for Greece to reduce its budget deficit and other risk factors would also likely keep investors cautious.
Other events expected this week include congressional testimony on Wednesday by Federal Reserve Chairman Ben Bernanke.
Bernanke will speak about unwinding of emergency Fed liquidity programmes and implications for the economic recovery.
Also, traders said market players are wary that China may take a further tightening step before a week-long holiday next week.
The dollar index, a measure of its performance against six major currencies, slipped 0.2 percent to 80.164 <.DXY>.
The greenback was up 0.2 percent against the yen at 89.46 yen.
Among higher-yielding currencies, the Australian dollar was trading around $0.8696, up 0.6 percent on the day and off a five-month low of $0.8578 touched last week.
The New Zealand dollar was at $0.6882, up 0.8 percent on the day.
(Additional reporting by Kaori Kaneko; Editing by Michael Watson)