The rupee opened marginally lower at 64.97 per dollar as against the previous closing level of 64.96 at the Forex market and moved down further to 64.99 on initial dollar demand from banks and importers.
However, it recovered from initial losses to 64.93 on selling of dollars by exporters before ending at the same opening level of 64.97, showing a mere loss of one paise or 0.02 per cent.
The domestic unit hovered in a range of 64.93 and 64.99 per dollar during the day.
Meanwhile, the forex dealers were in a wait-and-watch mode ahead of the Federal Reserve meeting, which is starting from Tuesday.
The dollar index was trading lower by 0.07 per cent against a basket of six currencies in the late afternoon trade.
In the global market, dollar fell against most of its rivals on Monday on weaker-than-expected US data on housing and manufacturing sectors.