However, caution over a possible rise in retail inflation levels due to higher crude oil prices capped gains.
Index-wise, the broader Nifty50 of the National Stock Exchange (NSE) closed at 10,842.85 points -- up by 55.90 points or 0.52 per cent -- from its previous close of 10,786.95 points.
Similarly, the barometer 30-scrip Sensitive Index (Sensex), which had opened at 35,525.30 points, ended in the green. It settled at 35,692.52 points -- higher by 209.05 points or 0.59 per cent -- from its previous session's close of 35,483.47 points.
The Sensex touched a high of 35,743.08 points and a low of 35,479.07 points during the intra-day trade. The BSE market breadth was bullish with 1,440 advances and 1,224 declines.
"Markets rallied strongly on Tuesday on buying in index heavyweights. Sentiments were boosted after Trump and Kim Jong Un signed an unspecified document in Singapore," said Deepak Jasani, Head of Retail Research at HDFC Securities.
Geojit Financial Services' Head of Research Vinod Nair said: "Market edged higher supported by positive outcome from US-N.Korea summit which may lead to an end of conflicts in Korean peninsula.
"However, global market remains mixed ahead of US Fed, ECB (European Central Bank) and BoJ (Bank of Japan) policy meeting during the week."
On the currency front, the Indian rupee weakened by seven paise against the US dollar to 67.49, from its previous close at 67.42.
Investment-wise, provisional data with exchanges showed that foreign institutional investors sold scrip worth Rs 1,168.88 crore while the domestic institutional investors bought stocks worth Rs 1,327.45 crore.
Sector-wise, the S&P BSE healthcare index gained 262.17 points, the capital goods index rose by 220.78 points and the banking index ended 204.94 points higher.
On the other hand, S&P BSE metal index was down by 76.85 points, followed by the basic materials and the telecom indices which were marginally down, by 9.24 points and 3.75 points respectively.
The major gainers on the Sensex were Dr Reddy's Lab, up 5.23 per cent at Rs 2,190.25; State Bank of India, up 3.36 per cent at Rs 282.85; Hindustan Unilever, up 2.41 per cent at Rs 1,640.45; IndusInd Bank, up 2.41 per cent at Rs 1,950.45; and Hero MotoCorp, up 2.11 per cent at Rs 3,688.75 per share.
The top losers were Bharti Airtel, down 1.98 per cent at Rs 381.05; Tata Steel, down 1.52 per cent at Rs 579.80; Coal India, down 1.49 per cent at Rs 283.50, ONGC, down 1.10 per cent at Rs 171.35 and Yes Bank, down 0.98 per cent at Rs 332.40 per share.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)