The rupee closed at 155.05/15 per dollar, compared with Monday's close of 154.95/155.00.
The rupee hit a record low of 155.90 per dollar on Feb. 14.
"Today the trading was dull as there were not much of import bills or remittance inflows as everybody is waiting to see the real impact of the state of emergency and violence," said a dealer.
Indian ocean island nation declared a nationwide state of emergency for 10 days on Tuesday to stop the Buddhist-Muslim violence from spreading.
The local currency has weakened 1.04 percent so far this year, after declining 2.5 percent last year and 3.9 percent in 2016.
It is expected to be pressured by continued importer demand for dollars ahead of the traditional New Year in April, dealers said.
Gradual depreciation in the rupee and higher volatility this year are expected on account of debt repayments by the government, dealers added.
The government must repay an estimated 1.97 trillion rupees ($12.68 billion) in 2018 - a record high - including $2.9 billion of foreign loans and a total of $5.36 billion in interest.
Foreign investors sold government securities worth a net 3.2 billion rupees in the week ended Feb. 28, central bank data showed.