The rupee depreciated by 10 paise to 54.45 against the US dollar in early trade today on the Interbank Foreign Exchange due to appreciation of the American currency against the euro and other currencies in overseas markets.Dealers attributed the rupee's fall to dollar gains against the euro overseas and sustained demand for the American currency from importers. They said, however, a higher opening of the domestic equity market capped rupee's losses.The rupee had gained 33 paise to touch a three-week high against the dollar at 54.35 in yesterday's trade on firmforeign fund inflows, after US lawmakers passed a bill which has averted the fiscal cliff.