The rupee is trading at 61.92/93 versus Friday's close of 61.7625/7725. Pair earlier fell to 61.6550.
Euro close to a two-year trough against the dollar as investors bet the ECB will ease monetary policy more aggressively.
Traders say good demand for the greenback also seen from state-run banks, offsetting foreign fund inflows into shares.
Nifty ends up 0.6 percent.
Asian shares broadly higher on prospects of further policy stimulus in China and Europe.
(Reporting by Swati Bhat)