Although both indexes are well below the record highs hit on Friday, when the Nifty gained as much as 1.2 percent before pulling back, brokers continue to raise their targets for the year.
Overseas investors bought Indian shares worth of 36.34 billion rupees ($615.6 million) on Friday, marking their biggest single-day purchase since March, provisional exchange data shows.
However, analysts outpoint that stocks are now looking overbought as per technicals, which may lead to some consolidation in the near term.
The BSE Sensex was trading up 0.6 percent while the Nifty gained 0.5 percent as of 11.53 a.m.
Stock markets: Morning trade
The benchmark BSE Sensex trimmed its initial gains but was still trading up by 154 points in morning trade amid buying in realty, capital goods, power, refinery, banking and metal sector stocks and persistent foreign capital inflows.
Foreign institutional investors (FIIs) bought shares worth a net Rs 3,634.82 crore on Friday, as per provisional data from the stock exchanges.
Investors are hoping that the BJP-led government will be better at getting things done and would be more business-friendly than the Congress-led coalition government, which was in power during the past ten years.
The 30-share Sensex opened higher at 24,340,32 and moved up further to 24,427.10 on strong initial buying.
But, it fell afterwards to 24,238.29 before quoting at 24,276.04 points at 1000 hours, still showing a gain of 154.30 points, or 0.64 per cent, from last weekend's level.
The NSE 50-share Nifty also moved up by 38.25 points, or 0.53 per cent, to 7,241.25 at 1000 hours.
Major gainers were Coal India (5.45 per cent), BHEL (4.58 per cent), Tata Power (4.36 per cent), ONGC (3.39 per cent), SBI (3.20 per cent), SSLT (3.078 per cent) and Larsen (2.88 per cent).
Meanwhile, Asian stocks were trading mostly lower today after data showed a slowdown in China's housing market.
Key benchmark indices in South Korea, Taiwan, Hong Kong and China fell by 0.04 to 1.09 per cent while indices in Singapore and Japan rose by 0.07 to 0.86 per cent.