In early trade, the rupee fell 14 paise to 77.69 against the US dollar.
On Friday - the previous trading day - the rupee hit an intraday low of 77.63/$.
The rupee has dropped 65 paise in a week due to a stronger dollar index, risk-off sentiment, and outflows of foreign funds.
Meanwhile, ahead of their quarterly earnings results, telecom operator Bharti Airtel and refiner Indian Oil Corp rose 0.3 percent and 1%, respectively, on Tuesday.
The Reserve Bank of India has increased up its intervention in the currency market which slowed the pace of the fall. Following Russia's invasion of Ukraine, the Indian currency, which has depreciated by around 4% in 2022, came under pressure. Since the war began in late February of this year, the foreign reserves have dropped by around $35 billion.
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