Forex traders said a firming US currency overseas and continued outflow of foreign funds from the Indian market also contributed to the weakness in the rupee.
In the interbank foreign exchange market, the rupee opened with a slight rise at 76.48 against the US dollar. In early trade, it had strengthened its position and touched the level of 76.35.
But after the afternoon, it saw a declining trend and it lost its strength under the influence of domestic markets. The rupee also remained at an upper level of 76.35 and a low of 76.51 during trading.
At the end of trading, it closed at 76.51, which shows a slight decline of one paise.
Global oil benchmark Brent crude futures fell 2.61 per cent to $104.34 per barrel.
Meanwhile, the dollar index, which gauges the strength of the US dollar against six major currencies, rose 0.43 per cent to 103.37.
In the domestic stock markets, the 30-share BSE Sensex was down 84.88 points, or 0.15 per cent, at 56,975.99. On the other hand, NSE Nifty saw a decline of 33.45 points or 0.20 percent.
Foreign institutional investors (FIIs) continue to withdraw from the Indian stock markets. According to stock market data, foreign investors sold shares worth Rs 3,648.30 crore on Friday.