Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.22 per cent to 96.96.
The rupee opened at 75.51 against the US dollar, gained further ground and finally closed for the day at 75.04 against the US dollar, up 56 paise over its previous close.
Forex traders said that these measures announced by RBI Governor Shaktikanta Das would provide the much needed liquidity and ease the financial stress caused by the pandemic.
Forex traders said the rupee is trading in a narrow range as losses in the greenback supported the rupee, while weak domestic equities weighed on the local unit.
Investors are also awaiting cues from CPI dada for March and the minutes of the Monetary Policy Committee's latest meeting scheduled to be released later in the day.
Forex traders said the rupee continued to consolidate in a narrow range ahead of inflation and industrial production number that will be released on Wednesday.
The rupee opened weak at 71.51 at the interbank forex market, down 18 paise over its previous close.
Gains in the US dollar against the world currencies also weighed on the rupee sentiment.
Traders said that the appreciation in the rupee was largely on the back of positive global cues such as easing US-China tensions.
At the interbank foreign exchange, the rupee opened weak at 71.01, showing a decline of 14 paise over its previous closing.
Forex traders said easing crude prices, weakening of the American currency and foreign fund inflows strengthened investor sentiments.
The Indian rupee on Thursday had closed at 71.31 against the dollar.
At the Interbank Foreign Exchange, the rupee opened weak at 71.08 then fell to 71.11 against the US dollar, showing a decline of 13 paise over its previous closing.
The dollar's gains against other currencies overseas on worries over escalating trade tensions between the US and China, also impacted the rupee sentiment.