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.
"Indian Rupee touched a 11-month high, as the currency is benefiting from positive sentiments post a decisive mandate at the center. Foreign inflows continue in the stock market, as investor chase the best performing market in Asia. Indian equity indices, Sensex and Nifty, are up over a percent. Banking and infrastructure and PSU stocks are leading the surge, as investors look to capitalize from the expected change in policy environment," said Anindya Banerjee, currency analyst, Kotak Securities.
Over the near term, Indian Rupee can continue to appreciate towards 57.50/58.00 levels, as foreign investors continue to show confidence in the Indian equity market.
"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 247 billion rupees ($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 BSE and NSE indexes hitting record closing highs on continued optimism about substantial reforms by the incoming BJP.
Overseas investors bought a net 36.34 billion rupees of local shares on Friday, their biggest single-day purchase since March, provisional exchange data showed.
In the offshore non-deliverable forwards, the one-month contract was at 58.89, while the three-month was at 59.49.
FACTORS TO WATCH
* Yen breaches key level, hints at breakout higher
* Emerging stocks just off 6-1/2 mth highs on China
* China, Europe drag world stocks lower; dlr slips
* Foreign institutional investor flows
* Rupee ends at 58.59/60 per dlr vs 58.79/80 on Fri
* Small support for rupee seen around 58.30/$1 level: South Indian Bank
* Rupee seen in 58.50 to 59.00 per dlr range for the week: dealers
($1 = 59.0300 Indian Rupees)