The rupee resumed higher at 61.08 per dollar as against the last closing level of 61.39 at the Interbank Foreign Exchange (Forex) Market.
It firmed up further to 61.06 per dollar. However, the local currency trimmed its early gains and was quoted at 61.27 per dollar at 1040 hours.
It moved in a range of 61.06 and 61.29 per dollar during morning deals.
The BSE benchmark Sensex rose by 210.23 points or 1.04 per cent to 20,483.14 at 1055 hours.
In New York market, the US dollar jumped to its highest level against the Japanese yen yesterday since the partial government shutdown began, a sign of investor optimism as House Republican leaders said they would propose a temporary debt-ceiling extension ahead of a meeting with President Barack Obama.