Modi is likely to return to power with an even bigger majority in parliament after a mammoth election that ended on Sunday, the exit polls showed, a far better showing than expected in recent weeks.
The rupee put on as much as 1.2% to 69.36 against the dollar, its best intraday percentage gain since Dec. 18.
Rushabh Maru, currency and commodity analyst with Anand Rathi Shares and Stock Brokers, said most exit polls have projected a "thumping majority" for the ruling government.
"This ensures policy continuity and required stability. Hence it will attract long term investors," he said. Votes will be counted on Thursday.
If the outcome matches the exit polls, "then the rupee may head towards 68 levels in coming sessions," added Maru.
The rupee, which was under continual pressure in 2018 due to higher oil prices and global risks, has gained about 0.3 percent against the dollar this year.
The South Korean won put on as much as 0.4% to 1,191.50 against the dollar after a finance ministry official said authorities are watching trades to see if large-scale transactions, or herd-like behaviour, causes distortions in the dollar-won exchange rate.
In the broader market, the tensions around U.S.-China trade talks continued to keep investors away from making big bets on emerging markets.
The Chinese yuan bounced from a 5-1/2-month low against the dollar hit last week, helped by a firmer-than-expected midpoint and the central bank's pledge to keep the currency stable.
Prior to market opening on Monday, the People's Bank of China lowered its official midpoint for the eighth straight day to 6.8988 per dollar, 129 pips weaker than the previous fix of 6.8859. Monday's fixing was the softest since Dec. 24.
The yuan strengthened up to 0.3%, its best intraday percentage gain in over a week. The Philippine peso and the Indonesian rupiah were little changed.
The Taiwan dollar weakened as much as 0.2% ahead of April data on export orders, an indicator of demand for Asia's hi-tech gadgets.
Taiwan's export orders likely declined for a sixth month in April but at a slower pace than in March, a Reuters poll showed, as the island's manufacturers keep struggling with a drop in global tech demand.
Markets in Singapore, Thailand and Malaysia were closed on Monday for a holiday. In offshore trading, the Singapore dollar strengthened slightly.