The spot rupee closed at 158.20/30 per dollar, compared with Monday's close of 157.90/158.05.
"There was usual importer dollar demand, but it was piled up due to two days of holidays," a currency dealer said.
"We expect the local currency to depreciate gradually because of more imports than exports."
Dealers said the rupee will be under pressure with exporters staying on the sidelines in anticipation of a fall in the unit, in line with other emerging market currencies.
A possible slump in the country's top agriculture export, tea, due to heavy monsoon rains also weighed on sentiment.
Dealers expect lower dollar inflows from tea exports to weigh on the currency, apart from debt repayments by the government, and see the rupee declining between 4 percent and 5 percent this year.
The rupee hit an all-time low of 158.50 per dollar on May 16. The currency has declined 0.25 percent so far this month after a 1.5 percent fall in April. It has fallen 3 percent so far this year.
The pressure on the currency is unwarranted as gross external reserves are at $9.1 billion and the real effective exchange rate indexes indicate that the currency is competitive, the central bank had said.
Foreign investors sold government securities worth a net 457 million rupees ($2.89 million) in the week ended May 23, bringing the outflow so far this year to 16.2 billion rupees, central bank data showed.