The rupee was down despite the weakening of dollar against other currencies in the overseas forex markets.
The rupee resumed higher at 55.80 a dollar after yesterday's closing level of 55.91 at the Interbank Foreign Exchange (Forex) Market.
However, it failed to maintain gains and touched a low of 56.02 at 1040 hrs on renewed dollar demand from banks and importers.
The rupee moved between 55.80 and 56.02 a dollar during the morning deals.
In New York, the euro advanced against the US dollar yesterday after a news report said European Central Bank policy makers would consider buying distressed government bonds in a more currency-friendly way.
Meanwhile, the BSE 30-stock index, Sensex was slightly up by 7 points or 0.04 per cent at 1050 hrs.