The domestic unit moved in the tight range of 83.70-83.72 in early trade.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, declined 0.19 per cent to 104.36.
Brent crude futures -- the global oil benchmark -- rose 1.49 per cent to USD 79.80 per barrel.
All eyes will be on the US Fed rate announcement later in the day. Expectations are ripe that the Federal Reserve might signal a rate cut as early as September.
In the domestic
Foreign institutional investors were net sellers in the capital markets on Tuesday, offloaded shares worth Rs 5,598.64 crore, according to exchange data.