At 3:04 am, the Sensex traded 111.29 points - or 0.27 per cent - higher at 41,970.98 while the Nifty was up 39.65 points - or 0.32 per cent - at 12,369.20.
Top percentage gainers on the 50-scrip benchmark index at the time were Vedanta, Britannia, ITC, Hero MotoCorp and Zee Entertainment, up between 1.62 per cent and 2.87 per cent. Thirty eight stocks on the Nifty moved higher at the time.
On the other hand, Yes Bank, IndusInd Bank, UPL, Kotak Mahindra Bank and SBI - trading between 0.88 per cent and 8.55 per cent lower - were the top losers.
HDFC and ITC were the top contributors to the gain in Sensex, together accounting for a rise of nearly 90 points in the index.
Official data released after market hours on Monday showed consumer inflation - gauged by the Consumer Price Index (CPI) - stood at 7.35 per cent in December, the worst level recorded since August 2014. That dashed hopes of further monetary easing by the central bank.
The Reserve Bank of India (RBI)'s next bi-monthly policy review is due in February. The RBI, which tracks consumer consumer inflation data primarily for formulating its monetary policy, reduced the repo rate by 135 basis points in 2019 but kept it on hold in a surprise move in December citing concerns about inflation.
Equities in other Asian markets rose as signs of goodwill between the US and China supported optimism for global growth, with the world's two biggest economies preparing to formalise a trade-war truce.
MSCI's world shares gauge hit a fresh all-time high, while MSCI's broadest index of Asia-Pacific shares outside Japan drifted higher. Japan's Nikkei added 0.8 per cent and hit its highest level recorded in a month.
The US Treasury Department on Monday said China should no longer be designated a currency manipulator - a label it applied as the yuan slid in August. China, meanwhile, has allowed the tightly managed currency to climb to its highest point since July.
On Monday, the Sensex and Nifty registered new record closing highs. The Sensex ended 259.97 points - or 0.62 per cent - higher at 41,859.69 whereas the Nifty settled at 12,329.55, up 72.75 points - or 0.59 per cent - from its previous close.
Domestic stock markets recovered early weakness to new all-time highs in late afternoon deals on Tuesday, tracking gains in global peers where equities registered record levels on optimism on the US-China trade front. The S&P BSE Sensex index rose as much as 134.57 points to hit an all-time high of 41,994.26, and the broader NSE Nifty benchmark rose 44.7 points to a record 12,374.25, as the markets broke through after moving in a tight range for most of the session. However, gains in consumer goods, auto and metal were offset by losses in select financial stocks.