Since early October, the oil price has fallen by a quarter to below $70 a barrel, its lowest in eight months.
At 10.25 am, the Sensex was trading down by 92.12 points or 0.26 per cent at 35,052.37 and the Nifty down 17.9 points or 0.17 per cent at 10,564.60.
The Reserve Bank of India will buy 120 billion rupees ($1.65 billion) of government bonds on Thursday via open market operations.
US West Texas Intermediate (WTI) crude oil futures were at $55.66 per barrel at 0043 GMT, down 3 cents from their last settlement.
US crude futures dived 7 per cent the previous day, suffering their biggest one-day loss in more than three years.
Walmart on Tuesday announced that Flipkart CEO Binny Bansal has resigned over allegations of serious personal misconduct.
According to a press statement released by Walmart, Bansal's decision comes after an independent investigation was launched against him on over an allegation of 'serious personal misconduct.'
The rupee staged a strong comeback by strengthening 37 paise to 72.52 (intra-day) against the American currency.
The consumer price index (CPI)-based inflation fell to a one-year low of 3.31 per cent in October 2018, from 3.7 per cent in September 2018 and 3.58 per cent in October 2017.
Further impacting market sentiments, the rupee again breached the 73-mark, dropping 57 paise (intra-day) to 73.07 against the dollar.
Retail inflation fell to a one-year low of 3.31 per cent in October on the back of cheaper kitchen staples, fruits and protein-rich items, official data released Monday showed.
RBI Deputy Governor Viral Acharya had in a speech last month talked about the independence of the central bank, arguing that any compromise could be "potentially catastrophic" for the economy.
Investment bank Goldman Sachs also fell 7.5 per cent, weighing on the financial sector
The rates of the fuel across India have been slashing due to the slip in the prices of crude oil prices.
Global gas demand would increase by 1.6 per cent a year to 2040 and would be 45 per cent higher by then than today, IEA said.