The Indian rupee opened 5 paise higher at 71.26 per US dollar on December 31 against the previous day's close of 71.31.
On December 30, the rupee appreciated by 4 paise to settle at 71.31 against the US currency amid the weakening of the US dollar in overseas markets even as crude oil prices surged.
Subdued domestic equity markets and high crude oil prices restricted the gains in the rupee, analysts said.
Jateen Trivedi, Senior Research Analyst (Commodity & Currency) at LKP Securities is of the view that rupee may see a dull trading session between 71.25-71.45 on account of year-end holidays.
The rupee has been trading in a flat range between 71.28-71.41 for some days mainly due to oil importers buying dollars frequently for their month-end outflows.
Some foreign banks are selling USD-INR which is also inducing some volatility.
In the second special open market operation (OMO), the Reserve Bank of India on December 30 bought Rs 10,000 crore of long-term government securities and sold Rs 8,501 crore of three short-term bonds.
The RBI had announced to purchase and sell simultaneously government securities under Open Market Operations (OMO) for Rs 10,000 crore each, last week.