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However, continued central bank dollar-buying capped broader gains, with traders expecting the Reserve Bank of India to continue stepping in as it looks to build up its foreign exchange reserves.
Data on Friday showed India's dollar reserves surged to a more than two-year high of $313.83 billion for the week to May 9, the highest since Nov. 11, 2011.
"In the near term, bullishness in rupee to continue for sometime, and any upticks towards 60 per dollar are likely to be sold off while small support is seen around 58.30 level," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
The partially convertible rupee closed at 58.59/60 per dollar after hitting 58.32, its strongest since June 18. The pair had closed at 58.79/80 on Friday.
Earlier in the day, rating agency Moody's Investor Service said the Bharatiya Janata Party's win was credit positive for India as it boosts the prospect that a stable government will address the country's economic challenges.
Also, Indian state-oil refiners will receive Rs 24,700 crore ($4.18 billion) worth of planned subsidy payouts in three tranches, including one worth 80 billion rupees that was already paid on May 16, a senior company official told Reuters on Monday.
The stronger rupee tracked gains in domestic shares, with the Sensex and Nifty hitting record closing highs on continued optimism about substantial reforms by the incoming BJP.
Overseas investors bought a net Rs 3,634 crore-worth of local shares on Friday, their biggest single-day purchase since March, provisional exchange data showed.
In the offshore non-deliverable forwards
