At the interbank foreign exchange market, the local unit opened weak at 83.25 and oscillated between a high of 83.23 and a low of 83.59 against the greenback during the session.
The domestic currency finally closed at 83.59 (provisional) against the dollar, registering a fall of 45 paise from its previous close.
On Monday, the Rupee closed at 83.14 against the US dollar.
Counting of votes on Tuesday indicated disappointing results for the BJP-led NDA in the Lok Sabha elections, which appears to be losing heavily in its strongholds of Uttar Pradesh, Haryana and Rajasthan although it is expected to form the government with about 290 seats.
On its own, the Bharatiya Janata Party appeared to be falling below the majority mark with leads in 236 seats despite significant gains in Odisha, Telangana and Kerala, giving some solace to the party after the unexpected losses in the Hindi belt.
Its rival INDIA alliance was leading in about 230 seats. In the last elections, the BJP had 303 seats on its own, while the NDA had over 350.
"The rupee depreciated...today as domestic markets fell sharply amid uncertainty over election results outcome. This may have also led to some sell-off by
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.17 per cent higher at 104.25.
Brent crude futures, the global oil benchmark, dropped 1.88 per cent to USD 76.89 per barrel.
On the domestic equity market, the 30-share
Foreign investors were net buyers of Indian equities on Monday as they purchased shares worth Rs 6,850.76 crore on a net basis. FIIs bought shares worth Rs 23,451.26 crore and sold equities worth Rs 16,600.50 crore in the cash segment.