The rupee resumed higher at 59.10 per dollar as against the last Friday's closing level of 59.17 at the Interbank Foreign Exchange market.
However, it immediately appreciated to 58.98 on bouts of dollar selling.
It hovered in a range of 59.10 and 58.98 per dollar before quoting at 59.03 at 1020 hours.
In New York market, the US dollar inched up against the Japanese yen last Friday, notching a weekly gain, in the wake of data showing the US economy added 217,000 jobs in May.