The rupee today fell marginally by 4 paise to trade at fresh one-week low of 53.95 against the US dollar in early trade on the Interbank Foreign Exchange due to appreciation of the American currency against the euro overseas and a weak opening in the domestic equity market.Increased month-end demand for the dollar from banks and importers also put pressure on the rupee. Dealers attributed the rupee's fall to dollar gains against the euro overseas and a lower opening in the stock market.The rupee had lost 23 paise to close at one-week low of 53.91 a dollar in yesterday's trade on heavy demand fromimporters for the American currency.