Forex traders said strengthening US dollar against some currencies overseas and lower opening of domestic equities weighed on the local unit.
However, fresh foreign fund inflows capped the losses for the domestic unit.
At the Interbank Foreign Exchange, the rupee opened on a weak note at 71.19 then fell further to 71.22 against the US dollar, showing a decline of 12 paise over its previous closing.
On Monday, the rupee had settled 7 paise higher at 71.10 against the US dollar.
Foreign funds bought shares worth Rs 223.44 crore from the capital markets on a net basis Monday, and domestic institutional investors also bought shares worth Rs 92.32 crore, provisional data showed.
The global benchmark, brent crude oil was trading 0.32 per cent higher at USD 60.12 per barrel.
Meanwhile, domestic equity market opened on a weak note. The 30-share BSE benchmark Sensex, was trading at 35,546.64, down 110.06 points in early trade. The wide-based Nifty was also trading lower by 42.70 points at 10,618.85.