The domestic unit had settled at 70.81 against the US dollar on Tuesday.
The Reserve Bank on Wednesday cut key interest rate for the fourth consecutive time, as it reduced repo rate by 35 basis points to 5.40 per cent to boost the slowing economy.
The six-member monetary policy committee (MPC) also maintained the 'accommodative stance' on the monetary policy.
Noting that inflation is currently projected to remain within the target over a 12-month ahead horizon, the MPC said since the last (June) policy, domestic economic activity continues to be weak, with the global slowdown and escalating trade tensions posing downside risks.
The RBI also revised real GDP growth for 2019-20 downwards to 6.9 per cent from 7 per cent in the June policy.
Meanwhile, brent crude futures, the global oil benchmark, fell 0.29 per cent to $58.77 per barrel, as US-China trade dispute rattled investor sentiments.
Foreign institutional investors (FIIs) remained net sellers in the capital markets, pulling out Rs 2,107.93 crore on Tuesday, as per provisional data.
Domestic bourses also witnessed heavy volatility and was trading higher by 46.61 points or 0.13 per cent at 37,023.46 and Nifty was trading at 10,951.50, up 3.25 points or 0.03 per cent.
Meanwhile, on the global front investors fretted as dispute between tow of the world's largest economies intensified over tariffs and currency.
China has meanwhile reported to have said that it is halting new purchases of US agricultural products after President Trump vowed last week to impose new tariffs on Chinese goods starting in September.