The 30-share Sensex ended up 30 points at 26,421 after hitting a record intra-day high of 26,531 and the 50-share Nifty ended 23 points higher at 7,898 after touching a fresh high of 7,919.
Domestic institutions were net buyers to the tune of Rs 490 crore while foreign institutiona investors were net buyers to the tune of Rs 473 crore on Monday, as per provisional stock exchange data.
According to the market regulator Sebi, mutual funds have invested over Rs 5,400 crore, twice the Rs 2,685 crore invested by foreign funds between July 24 and August 13.
The Indian rupee firmed up against the US dollar on the back of dollar inflows after domestic stock markets surged to record highs. Forex markets were closed for trading on Friday and Monday for holidays.
The Indian rupee is currently tad higher at Rs 60.75 compared to Thursday's close of Rs 60.76.
Asian markets ended higher on Tuesday tracking overnight gains in the US and easing of geopolitical tensions in Ukraine.
Japanese shares edged higher amid upbeat US housing data while weakness in the yen also boosted sentiment and the benchmark Nikkei ended up 0.8%.
Chinese shares recovered from the day's lows and the Shanghai Composite ended up 0.3% while Hang Seng gained 0.7%. Singapore's Straits Times ended up 0.2%.
European shares were also trading firm after geopolitical tensions in the Ukraine eased. The CAC-40, DAX and FTSE-100 were up 0.4-0.9% each.
The BSE Auto was the top sectoral gainer to end over 2% followed by Capital Goods, Power, Realty, Bankex and Healthcare indices.
Auto stocks gained on the back of encouraging sales growth in July.
Auto sales in India rose for the second straight month, according to July sales data released by individual auto makers, suggesting that a recovery may have begun to take hold in the sector after a two-year slump.
Analyst expects the upcoming festive season to set the pace of demand recovery especially in cars/two-wheelers,
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