The rupee opened lower at 63.66 per dollar at the Interbank Foreign Exchange (forex) as against 63.64 previously. It depreciated further to 63.68 before it was quoting at 63.60 at 1220 hours.
The domestic unit moved in a range of 63.68 and 63.64 in morning deals.
Overseas, the US dollar was higher in early Asian trade while the euro got off to a cautious start with Greece's fate still hanging in the balance.