The dollar also gained other currencies, putting further pressure on the rupee.
The key equity indices - S&P BSE Sensex and NSE Nifty50- remained subdued during Tuesday's morning trade session as the Congress party started to take the lead in the Assembly elections in three key states of Rajasthan, Madhya Pradesh and Chhattisgarh.
The key indices - the S&P BSE Sensex and NSE Nifty50 - had a gap-down opening and subsequently shed over 500 points and 140 points respectively as investors were spooked on the surprise resignation of RBI Governor Urjit Patel on Monday evening.
On the currency front, the Indian rupee weakened to 72.24 against the US dollar from its previous close of 71.34.
At 10.30am, the Sensex traded at 34,666.06 points, lower by 293.66 points or 0.84 per cent from the previous close.
Against the UAE dirham, the rupee was trading at 19.67 at 8:30am (UAE time), according to XE.com.
According to market observers, heavy selling pressure in banking, oil and gas and automobile stocks.
The Nifty50 on the National Stock Exchange traded at 10,414.20 points, lower by 74.25 points or 0.71 per cent from the previous close.
"Indian markets opened lower in line with expectations following RBI governor's abrupt exit on Monday evening," HDFC Securities' Retail Research Head Deepak Jasani told IANS.
"A recovery in the first few minutes of trade was based on initial trends from MP where BJP was faring better than Congress. However this proved to be short-lived as the lead of BJP narrowed soon," he said.
He further noted: "Markets would swing till around noon based on leads positions in MP, as the other four states are showing clear winners."
On Monday - the previous trade session - a global sell-off along with a rise in crude oil prices suppressed the key Indian equity indices deep into the red.
Consequently, the NSE Nifty50 had ended lower by 205.25 points or 1.92 per cent to 10,488.45 points, whereas the Sensex closed at 34,959.72 points - lower by 713.53 points or two per cent -- from its previous session's close of 35,673.25 points.