Forex dealers attributed the decline in rupee's value for the fourth trading day in a row to weakness in local equities amid fresh capital outflows.
The BSE benchmark Sensex fell by 167.54 points, or 0.90 per cent, to 18,451.33 in early trade.
The rupee lost 13 paise to close at a two-month low of 54.88 against the US dollar in the previous session on Monday.
The forex and money markets remained closed on Tuesday and Wednesday on account of "Diwali".