Forex traders said investors were optimistic about the US-China trade talks in October.
However, weak opening in domestic equities weighed on the local unit.
Domestic bourses opened on a cautious note on Tuesday with benchmark indices Sensex trading 113.23 points lower at 38,554.10 and Nifty down 20.70 points at 11,453.75.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.11 per cent to 99.48.
Market participants, however, said sustained foreign fund outflows weighed on local currency.
Foreign institutional investors (FIIs) remained net sellers in the capital market, pulling out Rs 469.40 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 1.83 per cent to trade at USD 60.78 per barrel.
The 10-year government bond yield was at 6.70 per cent in morning trade