The currency touched an all-time low of 172.95 per dollar on Tuesday, surpassing the previous record of 172.50 hit on Monday.
It closed at 172.40/60 per dollar on Monday.
The rupee has weakened 2.1 percent against the dollar so far this month, extending the 4.7 percent loss in September. It has declined 12.5 percent so far this year, Refinitiv Eikon data showed.