The rupee today fell by 11 paise to 53.78 against the dollar in early trade at the Interbank Foreign Exchange due to fresh demand for the US currency from importers and some banks.Forex dealers said euro's weakness against the dollar overseas also put pressure on the rupee.The rupee had gained 14 paise to end at 53.67 yesterday on consistent foreign fund inflows in local stocks amid fresh dollar selling by exporters and sustained weakness in the American currency overseas.