The currency had opened at 71.08 as traders exercised caution eyed US-China trade talks.
Trade groups from China and the US held “constructive" talks on relevant economic and trade issues of mutual concern in Washington during 19-20 September.
Government bond yields fell 4 basis points, after rising 15 basis points on Friday, as Finance Minister Nirmala Sitharaman allayed concerns about a near-term increase in government borrowing.
The yield on the 10-year Indian government bond ended at 6.749% compared with its previous close of 6.789%.
The benchmark equity index Sensex closed 2.83% higher at 39090.03 points. So far this year, the index has risen 8.4%.
In the year so far, the rupee has weakened 1.65%, while foreign investors have bought nearly $6.35 billion in Indian equities and $4.36 billion in debt.