The domestic unit on Thursday gained 28 paise to settle at 71.84 as investor sentiment revived after China and the United States said they will resume trade talks.
The domestic unit continued its winning momentum for a third session in a row on Friday, rising 12 paise to settle at 71.72.
The domestic unit on Friday appreciated by 38 paise to close at a two-week high of 71.42 on Friday led by a rally in domestic equities and renewed hopes of the US-China trade talks.
The domestic unit on Tuesday spurted by 54 paise, its biggest single-day gain in more than five months, to close at a one-week high of 71.48.
The currency settled at 72.02 to the US dollar, the lowest closing level since November 14, 2018, even as equities spurted more than 700 points at close on stimulus measures.
On Wednesday, the domestic currency rebounded from a six-month low to end at 71.27, up 13 paise.
The rupee's fall, though, was the sharpest in the region, followed by the Indonesian rupiyah, which lost 0.52 per cent
The government and RBI should address overvaluation
On Friday, it had dived 54 paise to close at an over six-week low of 69.60 as soaring crude oil prices and a fresh flare up in US-China trade tensions weighed on emerging market currencies.
A possible US sanction on India, if it goes ahead with buying Russian air defence system, also weighed on the sentiments
The record rally in domestic equities too helped the rupee
The RBI, meanwhile, fixed the reference rate for the dollar at 63.7375
The domestic unit on Friday marched higher for the seventh straight session to close at 70.92, up 22 paise.
The domestic unit on Monday recovered from day's low levels to close flat at 70.94 helped by foreign fund inflows into equities and lower global crude oil prices.
The domestic unit on Tuesday weakened by another 18 paise to settle at 71.78 against the US dollar as investors fretted over higher crude oil prices.
The domestic unit on Wednesday dipped three paise to close at 71.04 amid rising demand for the greenback vis-a-vis other currencies overseas, even as crude oil prices eased.
The domestic unit on Thursday strengthened by 16 paise to close at 70.88.
The domestic unit on Friday spurted by 32 paise to close at a nearly two-month high of 70.56.
The domestic unit on Tuesday dropped 20 paise to close at 71.07 as heavy selling in domestic equities, unabated foreign fund outflows kept investors edgy.
The domestic unit on Monday depreciated by 14 paise to close at 71.02 as profit booking in domestic equities and unabated foreign fund outflows kept investors edgy.