Forex traders said the rupee's rise was supported by dollar-selling by exporters and banks after the Chinese foreign ministry announced a mutually beneficiary agreement with the US.
At the Interbank Foreign Exchange (forex) market, the rupee opened lower at 70.91 and lost further ground to hit a low of 71.02 on a stronger dollar, strengthening US yields and worries about escalation in US-China trade war.
The local unit, however, pared the initial losses and finally settled the day on a higher note at 70.79 to the US dollar, up 8 paise.
"The rupee recovered sharply from the day's low in the second half after Chinese Foreign Ministry spoke of mutual beneficiary agreement between US President Donald Trump and his Chinese counterpart," V K Sharma, Head PCG & Capital Markets Group, HDFC Securities, explained.
"Our analysis suggests the fair value of the INR, based on productivity-adjusted REER, is in the 67-70 range. If the current trend of lower oil prices lasts through March 2019, we estimate end-FY19 INR against USD could trade in the 69-72 range," UBS Securities India Economist Tanvee Gupta Jain and Analyst Gautam Chhaochharia said in a research report.
Globally, Brent crude, the international benchmark, was trading 0.23 per cent higher at $60.62 per barrel.
The BSE benchmark Sensex rose for the second day, gaining over 159 points on hectic buying in banking and IT stocks as easing concerns on the macro-economic front bolstered investors' risk appetite. The broader NSE Nifty too witnessed a rise of 57 points.
The 10-year government bond yield remained almost flat at 7.732 per cent from its previous close of 7.727 per cent.
The dollar remained strong at almost two-week high of 97.19 against the basket of global currencies.
Meanwhile, foreign institutional investors (FIIs) made fresh purchases worth Rs 811.52 crore Tuesday, according to the provisional data.
The Financial Benchmark India Private Ltd (FBIL) set the reference rate for the rupee/dollar at 70.9065 and for rupee/euro at 80.4207. The reference rate for rupee/British pound was fixed at 90.8369 and for rupee/100 Japanese yen at 62.49.