On the domestic equity market front, the BSE Sensex was trading 277.80 points or 0.56 per cent higher at 50,069.92.
The RBI announced another round of USD 2 billion dollar-rupee swap on March 23 and up to Rs 1 lakh crore of long-term repo operations as and when required.
The domestic unit however could not hold on to the gains and was trading at 70.68 against the dollar at 0935 hrs.
Forex traders said rupee is trading in a narrow range as investors are also awaiting clarity on the US-China trade front.
The rupee opened weak at 71.10 at the interbank forex market and then fell further to 71.11, down 14 paise over its last close.
Rupee opened at 71.01 then fell to 71.03 against the US dollar, showing a decline of 9 paise over its previous closing.
Domestic bourses opened on a positive note on Monday with benchmark indices Sensex trading 120.08 points higher at 38,247.16.
Foreign institutional investors offloaded shares worth Rs 494.21 crore on Monday, according to provisional exchange data.
Domestic bourses opened on a negative note on Wednesday with benchmark indices Sensex trading 304.71 points down at 38,792.43 and Nifty lower by 82.05 points at 11,506.15.
Forex traders said fresh foreign fund inflows, higher opening in domestic equities and easing crude oil prices supported the rupee.
"This govt has had the benefit of low international oil prices since 2014, yet taxes on petrol and diesel were unprecedented and raised."
Michael Pillsbury, adviser to the White House on China policy, said that Trump would likely escalate the trade war by raising existing tariffs, if no deal is reached.
Crude oil prices witnessed a sharp spike after a weekend drone attack on Saudi Arabia cut into global energy supplies and halved the kingdom's oil production.
The domestic unit however could not hold on to the gains and was trading at 71.35 against the dollar at 0949 hrs.
The domestic unit pared some gains and was trading at 71.07 against the dollar at 0959 hrs. On Friday, the rupee had settled at 71.14 against the US dollar.
oreign institutional investors (FIIs) remained net sellers in the capital markets, pulling out Rs 638.28 crore on Tuesday, according to provisional exchange data.
The Indian rupee on Friday had closed at 70.78 against the US dollar.
The domestic unit pared some gains and was trading at 70.60 against the dollar at 0949 hrs.
Besides, a positive start of the equity markets also supported the rupee, forex dealers said.