The rupee closed at 157.60/80 per dollar on Tuesday, compared with Friday's close of 157.50/90. Markets were closed on Monday for a public holiday.
"Demand for dollars was there. Exporters were on the sidelines expecting further depreciation in line with regional currencies as the dollar is strengthening globally," a currency dealer said asking not to be named.
Officials from the central bank were not immediately available for comments.
The rupee hit an all-time low of 157.90 per dollar on Wednesday. It has declined 0.1 percent so far this month after a 1.5 percent fall in April.
The rupee will stabilise and the monetary authority will intervene to smooth high volatility as there is no reason for a weaker currency, Nandalal Weerasinghe, senior deputy governor at the central bank, said on Thursday.
The central bank said on April 26 that it would intervene to support the rupee when necessary and that there was no reason for the rupee to be under pressure given the country's record $10 billion foreign currency reserves.
Dealers said they expect the rupee to gradually weaken and face higher volatility this year due to debt repayments by the government.
Foreign investors sold government securities worth a net 5.7 billion rupees ($36.20 million) in the week ended May 2, bringing the outflow so far this year to 5.8 billion rupees, central bank data showed.
Crude oil prices retreated from their highest level in 3-1/2 years, while the dollar surged to its 2018 high.