The rupee was trading marginally weak by 2 paise at 61.73 against the dollar at 1.16 p.m. local time.
The domestic unit opened 24 paise weak at 61.95 per dollar against the previous close of 61.71 on fresh dollar demand from banks and importers amid strengthening of the US currency overseas.
Besides, weakness in the domestic equity market dampened the rupee sentiment.
Last week, the rupee had hit its three-week low against the dollar on account of sharp sell-off in the euro and a broad rally in the US dollar index.
According to Abhishek Goenka, Founder and CEO of India Forex, the rupee may weaken as RBI is likely to withdraw the special dollar swap window to oil marketing companies.
Call rates; G-secs
The overnight call money rate, rate at which banks borrow from each other for their short-term funding requirements, opened sharply higher at 8.7 per cent against the previous close of 8.3 per cent.
Yield on the 10-year benchmark government bond 7.16 per cent 2023 softened to 8.68 per cent from its previous close of 8.70 per cent. Bond prices opened at Rs 90.25 against Rs 90.15.